tag:blogger.com,1999:blog-79918920501402297182024-03-14T02:40:12.059-07:002013 S3-09 Maths Blogfarrellnahhttp://www.blogger.com/profile/12822697736062086588noreply@blogger.comBlogger178125tag:blogger.com,1999:blog-7991892050140229718.post-49679786469719657662014-01-29T03:38:00.001-08:002014-01-29T03:38:12.685-08:0029th Jan Recap<div class="separator" style="clear: both; text-align: center;">
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Homework = Statistics (b) Due next fridayShaun Nghttp://www.blogger.com/profile/07472085351698416501noreply@blogger.com0tag:blogger.com,1999:blog-7991892050140229718.post-5567457225525537372014-01-16T03:31:00.003-08:002014-01-16T03:31:52.302-08:00Probability summary<b>Probability: </b><br />
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Probability: How likely an event can occur<br />
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Probability = <u>The number of ways of achieving desired outcome</u><br />
Total number of possible outcomes<br />
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Event will definitely occur = 1<br />
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Event will never occur = 0<br />
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Event will not occur = 1 - probability of event occurring<br />
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Sample space: All the possible outcomes of an experiment<br />
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S = {a, b, c ...}<br />
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Sample point = 1 of the possible outcomes<br />
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Mutually exclusive: Both events cannot occur at the same time<br />
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Probability (A or B) = P(A) + P(B)<br />
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Independent events: Both events can occur at the same time; Outcome does not affect probability of outcome of other event<br />
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Probability (A and B) = P(A) x P(B)<br />
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Diagrams:<br /><br />
Probability diagrams:<br />
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Used for two independent events</div>
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Tree diagram: </div>
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Used for two or more events</div>
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Shaun Nghttp://www.blogger.com/profile/07472085351698416501noreply@blogger.com0tag:blogger.com,1999:blog-7991892050140229718.post-17903653761735314652013-09-16T08:13:00.003-07:002013-09-16T08:13:51.587-07:00Find my Centre - Authentic Task<br />
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<b><span style="color: #cc0000;">ACTIVITY <span style="font-size: large;">3</span></span></b></div>
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<b>Objective: </b></div>
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This is a collaborative activity to consolidate the learning of angles in a circle viz a viz APPLIED LEARNING MODE.</div>
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<b>ICT tools:</b> </div>
your choice (Geogebra, Geometer Sketch Pad etc)<br />
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<a href="http://www.delcam.tv/delcam-video.asp?VideoId=17" target="_blank"><img border="0" height="235" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQc8XdlALwG5fue9CSRj70W_JODU3argd1a_DmQFSFGLvoGAO4tmh5tANiVjUjtsqJq0dqjF1Nyt3MGwN0pm5aqOBdjuHyvI39pAB0G9kjMLt2bbxajUxaYkJjOYuUqbX0gCObcxOMpz0c/s320/Screen+Shot+2013-09-16+at+11.00.58+PM.png" width="320" /></a></div>
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<a href="http://mould making process" target="_blank">mould making process</a></div>
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<span style="font-family: Arial; font-size: 14pt;">TASK:</span><br />
<span style="font-family: Arial;"><span style="font-size: medium;">You are a mechanical engineer that is supervising a mould making process. You have just been tasked to replicate a circular object in your production line. The products must be precise (congruent of the highest degree) and must be mass produced efficiently at the shortest possible time with </span><span style="font-size: 19px;">minuscule</span><span style="font-size: medium;"> margin of error. </span></span><br />
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<span style="font-family: Arial;"><span style="font-size: medium;">The first task is to produce a mould by which all the objects will be replicated from. </span></span><br />
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<span style="font-family: Arial;"><span style="font-size: medium;">To facilitate the process, you are required to first determine how you would determine the following</span></span></div>
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<li><span style="font-family: Arial; font-size: 14pt; text-indent: -18pt;">centre of the circle</span></li>
<li><span style="font-family: Arial; font-size: 14pt; text-indent: -18pt;">radius of the circle / sphere</span></li>
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<span style="font-family: Arial; font-size: 14pt; text-indent: -18pt;">For the above activity, you are required to use the angles properties discovered in the topic. </span><br />
<span style="color: red; font-family: Arial; font-size: 14pt; text-indent: -18pt;">Do provide the logical reasoning in your answer.</span><br />
<span style="color: red; font-family: Arial; font-size: 14pt; text-indent: -18pt;">Post your solution in <u>blog page</u> assigned to you.</span><br />
<span style="font-family: Arial; font-size: 14pt; text-indent: -18pt;">Remember time is a factor so you have to plan your time very well.</span></div>
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Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-7991892050140229718.post-38730499897280029592013-09-16T07:05:00.002-07:002013-09-16T08:12:32.614-07:00Assessment 2013<span style="font-family: Arial, Helvetica, sans-serif;">Dear SSTudents,</span><br />
<span style="color: blue; font-family: Arial, Helvetica, sans-serif;"><br /></span>
<b><span style="color: blue; font-family: Arial, Helvetica, sans-serif;">1. Performance Task 2 (in lieu of Elementary Mathematics)</span></b><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">As mentioned earlier the deadline of the PT2 is 16 September 2013 @ 2359. To date many students have submitted their products with high quality questions and 'proof's. Effective use of ICT tools (google, Blog, Geogebra, Keynote, Powerpoint, Pretzi etc) have further enhanced the final product.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<b><span style="color: blue; font-family: Arial, Helvetica, sans-serif;">2. Paper 3 (in lieu of Additional Mathematics)</span></b><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">The assessment information will be as follows:</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">Date: <span style="color: red;"><b> 23 September </b></span> 2013 (Monday)</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"> (Please be punctual and ensure you have a heavier meal in the morning)</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">Time: 3.00 pm to 4.00 pm</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">Venue: Auditorium</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">Note that you are required to sit according to your classes and index numbers. The teachers will supervise you on this.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Logistic:</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">TI84 Graphic Calculator (or other approved GC model)</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">(no other calculator will be allowed)</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">Stationery - pen and ruler</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<b><span style="color: blue; font-family: Arial, Helvetica, sans-serif;">3. Information on EOY</span></b><br />
<span style="font-family: Arial, Helvetica, sans-serif;">Please refer to your class math blog or google site earlier entries on this.</span><br />
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<i><span style="color: blue; font-family: Arial, Helvetica, sans-serif;">All the best - you can do it because we have faith in you but do you!</span></i>Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-7991892050140229718.post-24481448904983108962013-09-15T07:52:00.000-07:002013-09-15T07:52:05.383-07:00Angles in a Circle - SELF DIRECTED<div class="separator" style="clear: both; text-align: left;">
<b><span style="color: #cc0000;">ACTIVITY 1</span></b></div>
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<b>Objective: </b></div>
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This is a self directed activity to consolidate the learning of angles in a circle. </div>
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<b>ICT tools:</b> </div>
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Math Blog for activity specifications</div>
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TI-Nspire CAS</div>
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tns file will be given at the beginning of session</div>
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<!--StartFragment-->
</div>
<div class="MsoNormal" style="text-align: left;">
<br />
<div class="separator" style="clear: both;">
<b><span style="color: #cc0000;">ACTIVITY <span style="font-size: large;">2</span></span></b></div>
<div class="separator" style="clear: both;">
<b><br /></b></div>
<div class="separator" style="clear: both;">
<b>Objective: </b></div>
<div class="separator" style="clear: both;">
This is a collaborative activity to consolidate the learning of angles in a circle viz a viz formative assessment. </div>
<div class="separator" style="clear: both;">
Error analysis will follow the assessment.</div>
<div class="separator" style="clear: both;">
<b><br /></b></div>
<div class="separator" style="clear: both;">
<b>ICT tools:</b> </div>
<div class="separator" style="clear: both;">
TI-Nspire CAS</div>
<div class="separator" style="clear: both;">
tns -based poll will be used to assess learning.</div>
<div class="separator" style="clear: both;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhasyupUxjBsYxsivMZvoMpMGuAjhwhGoh5Y3SvhMXGTvYqMF97UPlKRsh01hOQaRDhbyqPAGLV7W2GuReXuBJ5nIm3r1rnVY4LrTMM8n-YjlM-W0-VNrv8QS3Bd8V0ABRf0cGmay2UsMI/s1600/Screen+Shot+2013-09-15+at+10.45.53+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="290" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhasyupUxjBsYxsivMZvoMpMGuAjhwhGoh5Y3SvhMXGTvYqMF97UPlKRsh01hOQaRDhbyqPAGLV7W2GuReXuBJ5nIm3r1rnVY4LrTMM8n-YjlM-W0-VNrv8QS3Bd8V0ABRf0cGmay2UsMI/s320/Screen+Shot+2013-09-15+at+10.45.53+PM.png" width="320" /></a></div>
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<br /></div>
</div>
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<br /></div>
<div class="MsoNormal" style="text-align: left;">
<div class="separator" style="clear: both;">
<b><span style="color: #cc0000;">ACTIVITY <span style="font-size: large;">3</span></span></b></div>
<div class="separator" style="clear: both;">
<b><br /></b></div>
<div class="separator" style="clear: both;">
<b>Objective: </b></div>
<div class="separator" style="clear: both;">
This is a collaborative activity to consolidate the learning of angles in a circle viz a viz APPLIED LEARNING MODE.</div>
<div class="separator" style="clear: both;">
<b><br /></b></div>
<div class="separator" style="clear: both;">
<b>ICT tools:</b> </div>
TI-Nspire CAS<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhDUDHfpElfwOUFxOkUH3K5AWj7yaKVZEiv4lvfQmUH5Kr_UR5zqeGjC21MnwSz6-_D8AsyRlqxytl_jtvwLvOUVsAK4Eq2E7p4LvFlmGkZ4ldbepxXl77hLZbP8ZsyH98kEpAiEKE6dHk/s1600/Screen+Shot+2013-09-15+at+10.48.33+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="290" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhDUDHfpElfwOUFxOkUH3K5AWj7yaKVZEiv4lvfQmUH5Kr_UR5zqeGjC21MnwSz6-_D8AsyRlqxytl_jtvwLvOUVsAK4Eq2E7p4LvFlmGkZ4ldbepxXl77hLZbP8ZsyH98kEpAiEKE6dHk/s320/Screen+Shot+2013-09-15+at+10.48.33+PM.png" width="320" /></a></div>
<span style="font-family: Arial; font-size: 14.0pt; mso-bidi-font-size: 12.0pt;"><br /></span>
<span style="font-family: Arial; font-size: 14.0pt; mso-bidi-font-size: 12.0pt;">TASK:</span><br />
<span style="font-family: Arial; font-size: 14.0pt; mso-bidi-font-size: 12.0pt;">Given the object, determine how you would determine the
following</span></div>
<div class="MsoNormal" style="text-align: left;">
</div>
<ol>
<li><span style="font-family: Arial; font-size: 14pt; text-indent: -18pt;">centre of the circle</span></li>
<li><span style="font-family: Arial; font-size: 14pt; text-indent: -18pt;">radius of the circle / sphere</span></li>
</ol>
<div class="MsoNormal" style="text-align: left;">
<span style="font-family: Arial; font-size: 14pt; text-indent: -18pt;">For the above activity, you are required to use the angles
properties discovered in the topic. Do provide the logical reasoning in your
answer.</span></div>
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<div style="text-align: left;">
<br /></div>
Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-7991892050140229718.post-29102364297825001742013-09-03T17:30:00.003-07:002013-09-03T17:30:40.016-07:00Circle - Alternate Segment Theorem<br />
<h4>
<span style="font-weight: normal;">source: http://www.onlinemathlearning.com</span></h4>
<h2>
The Alternate Segment theorem states</h2>
<blockquote style="background-color: #d6d2d2; color: #000066; font-family: 'Courier New', Courier, monospace; font-size: 14px; line-height: 20px; margin: 12px 56px;">
<div class="definition" style="color: #990000; font-weight: bold;">
An angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.</div>
</blockquote>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="http://www.geogebratube.org/student/m18416" target="_blank"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhI4iq3T9UiVhvYet6ocYyQn67hk3U8NhOizWALiVhXtub6QFr569UxRabdxBG1ig8LFAafPD0TMbzT4NEewaI9aG71RX_pvfQAf00S-Gkj_DEVBN4T3UECwenIiP9pg1-s39mHEruLQPo/s1600/Screen+Shot+2013-09-04+at+8.14.58+AM.png" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://www.geogebratube.org/student/m18416" target="_blank">link to activity</a></div>
<br />
<div style="background-color: #d6d2d2; font-family: 'Lucida Sans Unicode', 'Lucida Grande', Verdana, Arial, sans-serif; font-size: 14px;">
Recall that a chord is any straight line drawn across a circle, beginning and ending on the curve of the circle.</div>
<div style="background-color: #d6d2d2; font-family: 'Lucida Sans Unicode', 'Lucida Grande', Verdana, Arial, sans-serif; font-size: 14px;">
In the following diagram, the chord <em>CE</em> divides the circle into 2 segments. Angle <em>CEA</em>and angle <em>CDE</em> are <span class="definition" style="color: #990000; font-weight: bold;">angles in alternate segments</span> because they are in opposite segments.</div>
<div style="background-color: #d6d2d2; font-family: 'Lucida Sans Unicode', 'Lucida Grande', Verdana, Arial, sans-serif; font-size: 14px;">
<img height="154" src="http://www.onlinemathlearning.com/image-files/alternate-segment-theorem1.gif" style="border: 0px solid rgb(221, 221, 221);" width="236" /> </div>
<div style="background-color: #d6d2d2; font-family: 'Lucida Sans Unicode', 'Lucida Grande', Verdana, Arial, sans-serif; font-size: 14px;">
The <strong class="definition" style="color: #990000;">alternate segment theorem</strong> states that an angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment</div>
<div style="background-color: #d6d2d2; font-family: 'Lucida Sans Unicode', 'Lucida Grande', Verdana, Arial, sans-serif; font-size: 14px;">
In terms of the above diagram, the alternate segment theorem tells us that angle<em>CEA </em>and angle <em>CDE</em> are equal.<br /><br /><br /></div>
<div class="highlight-step" style="background-color: #d6d2d2; color: #008800; font-family: 'Lucida Sans Unicode', 'Lucida Grande', Verdana, Arial, sans-serif; font-size: 14px;">
<strong><em>Example:</em></strong></div>
<div style="background-color: #d6d2d2; font-family: 'Lucida Sans Unicode', 'Lucida Grande', Verdana, Arial, sans-serif; font-size: 14px;">
In the following diagram, <em>MN</em> is a tangent to the circle at the point of contact <em>A.</em>Identify the angle that is equal to <em>x</em></div>
<div style="background-color: #d6d2d2; font-family: 'Lucida Sans Unicode', 'Lucida Grande', Verdana, Arial, sans-serif; font-size: 14px;">
<br /></div>
<div style="background-color: #d6d2d2; font-family: 'Lucida Sans Unicode', 'Lucida Grande', Verdana, Arial, sans-serif; font-size: 14px;">
<img height="160" src="http://www.onlinemathlearning.com/image-files/alternate-segment-theorem2.gif" style="border: 0px solid rgb(221, 221, 221);" width="229" /> </div>
<div style="background-color: #d6d2d2; font-family: 'Lucida Sans Unicode', 'Lucida Grande', Verdana, Arial, sans-serif; font-size: 14px;">
<br /></div>
<div class="highlight-subheading" style="background-color: #d6d2d2; color: #009933; font-family: 'Lucida Sans Unicode', 'Lucida Grande', Verdana, Arial, sans-serif; font-size: 14px;">
<strong><em>Solution:</em></strong></div>
<div style="background-color: #d6d2d2; font-family: 'Lucida Sans Unicode', 'Lucida Grande', Verdana, Arial, sans-serif; font-size: 14px;">
We need to find the angle that is in alternate segment to <em>x.</em></div>
<div style="background-color: #d6d2d2; font-family: 'Lucida Sans Unicode', 'Lucida Grande', Verdana, Arial, sans-serif; font-size: 14px;">
<em>x</em> is the angle between the tangent <em>MN</em> and the chord <em>AB.</em></div>
<div style="background-color: #d6d2d2; font-family: 'Lucida Sans Unicode', 'Lucida Grande', Verdana, Arial, sans-serif; font-size: 14px;">
We look at the chord <em>AB</em> and find that it subtends angle <em>ACB</em> in the opposite segment.</div>
<div style="background-color: #d6d2d2; font-family: 'Lucida Sans Unicode', 'Lucida Grande', Verdana, Arial, sans-serif; font-size: 14px;">
<img height="128" src="http://www.onlinemathlearning.com/image-files/alternate-segment-theorem3.gif" style="border: 0px solid rgb(221, 221, 221);" width="177" /> </div>
<div style="background-color: #d6d2d2; font-family: 'Lucida Sans Unicode', 'Lucida Grande', Verdana, Arial, sans-serif; font-size: 14px;">
So, angle <em>ACB</em> is equal to <em>x</em>.</div>
Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-7991892050140229718.post-83933360894019211782013-09-03T17:22:00.000-07:002013-09-03T21:52:24.212-07:00Circle - Cyclic Quadrilateral<div class="separator" style="clear: both; text-align: center;">
</div>
<div style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 1.75em; margin-bottom: 0.5em; margin-top: 0.4em; padding: 0px; text-align: -webkit-auto; vertical-align: baseline;">
source: <a href="http://www.artofproblemsolving.com/">http://www.artofproblemsolving.com/</a></div>
<div style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 13px; line-height: 1.75em; margin-bottom: 0.5em; margin-top: 0.4em; padding: 0px; text-align: -webkit-auto; vertical-align: baseline;">
A <b>cyclic quadrilateral</b> is a <a href="http://www.artofproblemsolving.com/Wiki/index.php/Quadrilateral" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #002bb8; text-decoration: none;" title="Quadrilateral">quadrilateral</a> that can be inscribed in a <a href="http://www.artofproblemsolving.com/Wiki/index.php/Circle" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #002bb8; text-decoration: none;" title="Circle">circle</a>. They have a number of interesting properties.</div>
<center style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 12px; line-height: 16px;">
<a class="image" href="http://www.artofproblemsolving.com/Wiki/index.php/File:Cyclicquad2.png" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #002bb8; text-decoration: none;"><img alt="Cyclicquad2.png" height="241" src="http://www.artofproblemsolving.com/Wiki/images/3/3e/Cyclicquad2.png" style="border: none; vertical-align: middle;" width="248" /></a></center>
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<span class="mw-headline" id="Properties">Properties</span></h2>
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In cyclic quadrilateral <a class="latex" href="http://www.artofproblemsolving.com/Forum/code.php?hash=fb2f85c88567f3c8ce9b799c7c54642d0c7b41f6&sid=2a23cab678f65d28876e667ee74ddccc" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #002bb8; text-decoration: none;"><img alt="ABCD" class="latex" src="http://data.artofproblemsolving.com/images/latex/f/b/2/fb2f85c88567f3c8ce9b799c7c54642d0c7b41f6.gif" style="border: none; margin: 0px; vertical-align: 0px;" title="ABCD" /></a>:</div>
<ul style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 12px; line-height: 16px; list-style-image: url(http://www.artofproblemsolving.com/Wiki/skins/aops/bullet.gif); list-style-type: square; margin: 0.3em 0px 0px 3em; padding: 0px; text-align: -webkit-auto;">
<li style="list-style-image: url(http://www.artofproblemsolving.com/views/aops/imageset/green_bulletpoint.gif); list-style-type: square; margin-bottom: 6px; padding: 0px;"><a class="latex" href="http://www.artofproblemsolving.com/Forum/code.php?hash=91604050363ceb3b5be3dd2c59c930a2e3fa6a55&sid=2a23cab678f65d28876e667ee74ddccc" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #002bb8; text-decoration: none;"><img alt="\angle A + \angle C = \angle B + \angle D = {180}^{o}" class="latex" src="http://data.artofproblemsolving.com/images/latex/9/1/6/91604050363ceb3b5be3dd2c59c930a2e3fa6a55.gif" style="border: none; vertical-align: -2px;" title="\angle A + \angle C = \angle B + \angle D = {180}^{o}" /></a></li>
<li style="list-style-image: url(http://www.artofproblemsolving.com/views/aops/imageset/green_bulletpoint.gif); list-style-type: square; margin-bottom: 6px; padding: 0px;"><a class="latex" href="http://www.artofproblemsolving.com/Forum/code.php?hash=cd0aba64745c5b558af5554556133da238c47242&sid=2a23cab678f65d28876e667ee74ddccc" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #002bb8; text-decoration: none;"><img alt="\angle ABD = \angle ACD" class="latex" src="http://data.artofproblemsolving.com/images/latex/c/d/0/cd0aba64745c5b558af5554556133da238c47242.gif" style="border: none; vertical-align: -1px;" title="\angle ABD = \angle ACD" /></a></li>
<li style="list-style-image: url(http://www.artofproblemsolving.com/views/aops/imageset/green_bulletpoint.gif); list-style-type: square; margin-bottom: 6px; padding: 0px;"><a class="latex" href="http://www.artofproblemsolving.com/Forum/code.php?hash=77e6bcfc5538d8ed952df2a3385ffd9ed630b21a&sid=2a23cab678f65d28876e667ee74ddccc" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #002bb8; text-decoration: none;"><img alt="\angle BCA = \angle BDA" class="latex" src="http://data.artofproblemsolving.com/images/latex/7/7/e/77e6bcfc5538d8ed952df2a3385ffd9ed630b21a.gif" style="border: none; vertical-align: -1px;" title="\angle BCA = \angle BDA" /></a></li>
<li style="list-style-image: url(http://www.artofproblemsolving.com/views/aops/imageset/green_bulletpoint.gif); list-style-type: square; margin-bottom: 6px; padding: 0px;"><a class="latex" href="http://www.artofproblemsolving.com/Forum/code.php?hash=ece76b3f12dea4aed5e214281185b56411f6e62a&sid=2a23cab678f65d28876e667ee74ddccc" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #002bb8; text-decoration: none;"><img alt="\angle BAC = \angle BDC" class="latex" src="http://data.artofproblemsolving.com/images/latex/e/c/e/ece76b3f12dea4aed5e214281185b56411f6e62a.gif" style="border: none; vertical-align: -1px;" title="\angle BAC = \angle BDC" /></a></li>
<li style="list-style-image: url(http://www.artofproblemsolving.com/views/aops/imageset/green_bulletpoint.gif); list-style-type: square; margin-bottom: 6px; padding: 0px;"><a class="latex" href="http://www.artofproblemsolving.com/Forum/code.php?hash=c0e409f526db77b37478a0aa9d992e2431394236&sid=2a23cab678f65d28876e667ee74ddccc" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #002bb8; text-decoration: none;"><img alt="\angle CAD = \angle CBD" class="latex" src="http://data.artofproblemsolving.com/images/latex/c/0/e/c0e409f526db77b37478a0aa9d992e2431394236.gif" style="border: none; vertical-align: -1px;" title="\angle CAD = \angle CBD" /></a></li>
</ul>
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<span class="mw-headline" id="Applicable_Theorems.2FFormulae">Applicable Theorems/Formulae</span></h2>
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The following theorems and formulae apply to cyclic quadrilaterals:</div>
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<li style="list-style-image: url(http://www.artofproblemsolving.com/views/aops/imageset/green_bulletpoint.gif); list-style-type: square; margin-bottom: 6px; padding: 0px;"><a href="http://www.artofproblemsolving.com/Wiki/index.php/Ptolemy%27s_Theorem" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #002bb8; text-decoration: none;" title="Ptolemy's Theorem">Ptolemy's Theorem</a></li>
<li style="list-style-image: url(http://www.artofproblemsolving.com/views/aops/imageset/green_bulletpoint.gif); list-style-type: square; margin-bottom: 6px; padding: 0px;"><a class="mw-redirect" href="http://www.artofproblemsolving.com/Wiki/index.php/Brahmagupta%27s_formula" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #002bb8; text-decoration: none;" title="Brahmagupta's formula">Brahmagupta's formula</a></li>
</ul>
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<a href="http://www.geogebratube.org/student/m18415" target="_blank"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhDfN3LLZIWYWxSCjQHSUZatrQFPGUx0TCSFY_dPnLzXjX7i9CcclnZl8HOJ7PPI8c224xq_lzs6cZg7Kn7QqDd6zG0szcF8zjg_-Vtgvd1rw_gSRz7Q5_WTrZ-APkjjlaPPns5WtGK5kc/s1600/Screen+Shot+2013-09-04+at+8.14.17+AM.png" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://www.geogebratube.org/student/m18415" target="_blank">the link</a></div>
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<br />Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-7991892050140229718.post-74494932116500507002013-09-03T03:07:00.001-07:002013-09-03T21:51:33.745-07:00Circle - angles @ centre & angles in same segment<h2>
<b>Class based activity:</b></h2>
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<b>Objectives: </b></div>
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to proof the validity of the following theorems through geometrical manipulations using Geogebra.</div>
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Theorem 1: Angle at the centre theorem</div>
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Theorem 2: Angle in a semi circle theorem</div>
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Theorem 3: Angles in the same segment</div>
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<b><span style="color: purple;">Activity 1:</span></b></div>
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Using the attached links explore the following:</div>
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a. the various permutations of Angle at the centre theorem</div>
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b. the relationship between Angle at the centre theorem and Angle in a semi circle theorem</div>
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<span style="color: purple;"><b>Activity 2:</b></span></div>
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Using the attached links explore the limitations of Angles in the same segment theorem.</div>
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<a href="http://www.geogebratube.org/student/m18414" target="_blank"><img border="0" height="218" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRvPz0H8nutP3_rxi89uBUP7a_R99-OsK5pBbnikcALqHP05EYRDXawK3SzEJaXwDRYLE7VQoPE71brPnXqgd3S3MX09FWJ25o_jGaUzy7PuMTnx7ZpQviwBrTXoVMHGz7tp57gCPu_G0/s320/Screen+Shot+2013-09-03+at+6.03.56+PM.png" width="320" /></a></div>
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<br /></div>
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<a href="http://www.geogebratube.org/student/m18414" target="_blank">link to activity</a>1</div>
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<a href="http://www.geogebratube.org/student/m18418" target="_blank"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJWSRsg9dgJM0g0GOp9DHNhTiOilHt39iexnqteKs-rEC0QrJS0s5ip2cRzCqtdPnQbLD1r7_eljrKpY6afEZn6lnLqZOcgf1ezwWT4EjftdPqIP8_UMSLoOo1ag9BkFPEzFnUDbbTD2Y/s320/Screen+Shot+2013-09-03+at+6.05.36+PM.png" width="320" /></a></div>
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<a href="http://www.geogebratube.org/student/m18418" target="_blank">link to activity</a>2</div>
<br />Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-7991892050140229718.post-42546325081468120922013-09-02T07:50:00.003-07:002013-09-02T08:00:55.709-07:00Circle - angle propertiessource: <a href="http://www.onlinemathlearning.com/angles-circle.html">http://www.onlinemathlearning.com/angles-circle.html</a><br />
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<iframe allowfullscreen="" frameborder="0" height="415" src="//www.youtube.com/embed/H2d3uVdFNmU" width="620"></iframe>
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Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-7991892050140229718.post-56438172872437974512013-09-02T07:44:00.004-07:002013-09-02T07:44:59.363-07:00Circle - Chord<div class="separator" style="clear: both; text-align: center;">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgL_BYjLu6KOy34k7ndLgmODw5jSfgdedYOkQesY4QmFOy7NEJ2AfYVQICcVrdfOVPtcrao54ggse02dLdb4bXAJRtpu1AN-21MWqkt2j5O-mfPEGHAOJBcNObjjBC_wA7Yutoya2RzPwg/s1600/Screen+Shot+2013-09-02+at+10.40.36+PM.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="206" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgL_BYjLu6KOy34k7ndLgmODw5jSfgdedYOkQesY4QmFOy7NEJ2AfYVQICcVrdfOVPtcrao54ggse02dLdb4bXAJRtpu1AN-21MWqkt2j5O-mfPEGHAOJBcNObjjBC_wA7Yutoya2RzPwg/s640/Screen+Shot+2013-09-02+at+10.40.36+PM.png" width="640" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuZLmbpKHnfcjpf67epXi2iJSrkJVbB22voOPt1md2zJEv7IniU6B9QbqrOLKkAKRUgLPzKlsKpUxIBz-E4ySvjBnHf_07Ee5CJAQBw1A_0R6mKXVcJIXGP_lFCmxfFOY1kO77PT9a8i8/s1600/Screen+Shot+2013-09-02+at+10.40.28+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" height="184" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuZLmbpKHnfcjpf67epXi2iJSrkJVbB22voOPt1md2zJEv7IniU6B9QbqrOLKkAKRUgLPzKlsKpUxIBz-E4ySvjBnHf_07Ee5CJAQBw1A_0R6mKXVcJIXGP_lFCmxfFOY1kO77PT9a8i8/s640/Screen+Shot+2013-09-02+at+10.40.28+PM.png" width="640" /></a><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2LlNzxpD_Aa4rdDyTcthsebjBHUTUs1YNRVNbhfHhhONr9dkHzBS4q5HU73k11bFHr5xQPRDCqJhbjX-AmlJ-ikoPQt0Pzky9NsvLJVvwIzRLs-H9cpmPDAj0TgJwaNJie2kqtefFjww/s1600/Screen+Shot+2013-09-02+at+10.40.44+PM.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="568" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2LlNzxpD_Aa4rdDyTcthsebjBHUTUs1YNRVNbhfHhhONr9dkHzBS4q5HU73k11bFHr5xQPRDCqJhbjX-AmlJ-ikoPQt0Pzky9NsvLJVvwIzRLs-H9cpmPDAj0TgJwaNJie2kqtefFjww/s640/Screen+Shot+2013-09-02+at+10.40.44+PM.png" width="640" /></a>Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-7991892050140229718.post-66475517969011815422013-09-01T21:23:00.001-07:002013-09-01T21:23:21.887-07:00Angles in a Circle<div class="separator" style="clear: both; text-align: center;">
Angles properties <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGcar6QtL_FuBTQMNTgwddm7VFdf25J4sqMRRukXEXmxouaT0XVavqKZ38sECBgaNdZome9BC-vfh322zAAfN6ODYl1IMDAQtFlBTiM8Anu88-Gp4Bx8CmctULhIkrmjRNWXEirLCffgk/s1600/Screen+Shot+2013-09-01+at+10.52.19+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="383" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGcar6QtL_FuBTQMNTgwddm7VFdf25J4sqMRRukXEXmxouaT0XVavqKZ38sECBgaNdZome9BC-vfh322zAAfN6ODYl1IMDAQtFlBTiM8Anu88-Gp4Bx8CmctULhIkrmjRNWXEirLCffgk/s640/Screen+Shot+2013-09-01+at+10.52.19+PM.png" width="640" /></a></div>
<br />Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-7991892050140229718.post-37014687575958074802013-08-31T07:21:00.001-07:002013-09-17T04:35:48.271-07:00Update on Assessment (i) PT2 (ii) P3 (iii) EOY<br />
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b style="background-color: yellow;">(1) Performance Task 2</b></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">This constitutes the Elementary Mathematics component of Assessment.</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">The performance task focuses on the topic of Geometrical Proof - Circle Properties. (please refer to Blog entry on <a href="http://sst2013-s309maths.blogspot.sg/2013/08/mathematics-performance-task-2.html" target="_blank">Mathematics Performance Task 2</a>)</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: #222222;">Deadline for submission is </span><b><span style="color: red;">Term 4 Week 1 Day 1 2359</span></b></span></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b style="background-color: yellow;">(2) Paper 3</b></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">This constitutes the Additional Mathematics component of Assessment.</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: #222222;">This will be conducted in </span><b><span style="color: red;">Term 4 (23 September 2013)</span></b><span style="color: #222222;">.</span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Students are expected to familiarise themselves with GC-TI84+.</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">(please refer to your Math teacher on information on use of GC-TI84+)</span></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><b style="background-color: yellow;">(3) End-of-Year Examination: Mathematics</b></span></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;">Information pertaining to the Maths exam has been communicated to the students in the GoogleSite (as well as the <a href="http://sst2013-s107maths.blogspot.sg/2013/08/end-of-year-exam-mathematics.html" style="color: #1155cc;" target="_blank">Maths blog</a>).</span></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><u>Elementary Mathematics paper 1</u></span></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;">Date:<b><span style="color: red;"> <span class="aBn" data-term="goog_1508903472" style="border-bottom-color: rgb(204, 204, 204); border-bottom-style: dashed; border-bottom-width: 1px; position: relative; top: -2px; z-index: 0;" tabindex="0"><span class="aQJ" style="position: relative; top: 2px; z-index: -1;">27 September 2013</span></span> </span></b>(<span class="aBn" data-term="goog_1508903473" style="border-bottom-color: rgb(204, 204, 204); border-bottom-style: dashed; border-bottom-width: 1px; position: relative; top: -2px; z-index: 0;" tabindex="0"><span class="aQJ" style="position: relative; top: 2px; z-index: -1;">Friday</span></span>)</span></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;">Duration: 1 hour 30 minutes</span></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><u>Elementary Mathematics paper 2</u></span></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;">Date:<b><span style="color: red;"> 30<span class="aBn" data-term="goog_1508903472" style="border-bottom-color: rgb(204, 204, 204); border-bottom-style: dashed; border-bottom-width: 1px; position: relative; top: -2px; z-index: 0;" tabindex="0"><span class="aQJ" style="position: relative; top: 2px; z-index: -1;"> September 2013</span></span> </span></b>(Monday)</span></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;">Duration: 2 hours</span></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><u>Additional Mathematics</u></span></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;">Date:<b><span style="color: red;"> <span class="aBn" data-term="goog_1508903472" style="border-bottom-color: rgb(204, 204, 204); border-bottom-style: dashed; border-bottom-width: 1px; position: relative; top: -2px; z-index: 0;" tabindex="0"><span class="aQJ" style="position: relative; top: 2px; z-index: -1;">4 October 2013</span></span> </span></b>(<span class="aBn" data-term="goog_1508903473" style="border-bottom-color: rgb(204, 204, 204); border-bottom-style: dashed; border-bottom-width: 1px; position: relative; top: -2px; z-index: 0;" tabindex="0"><span class="aQJ" style="position: relative; top: 2px; z-index: -1;">Friday</span></span>)</span></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;">Duration: 2 hours 30 minutes</span></div>
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<b><span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;">Table of Specification</span></b></div>
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<u><span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;">A. Elementary Mathematics</span></u><br />
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="color: #1a1a1a;">• </span>Numbers and the four operations (moe 1.1)</span></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="color: #1a1a1a;">• </span>Algebraic representation and formulae (moe 1.5)<span style="color: #1a1a1a;"></span></span></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="color: #1a1a1a;">• </span>Functions and graphs (moe 1.7)<span style="color: #1a1a1a;"></span></span></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="color: #1a1a1a;">• </span>Algebraic manipulation (moe 1.6)<span style="color: #1a1a1a;"></span></span></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="color: #1a1a1a;">• </span>Solutions of equations and inequalities (moe 1.8)</span></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="color: #1a1a1a;">• </span>Properties of circles (moe 2.3)<span style="color: #1a1a1a;"></span></span></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;"><span style="color: #1a1a1a;">• </span>Coordinate geometry (moe 2.6)<span style="color: #1a1a1a;"></span></span></div>
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;"><span style="color: #1a1a1a; font-size: x-small;">• Trigonometry</span></span></div>
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<u><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;"><span style="text-indent: -36pt;">B. </span><span style="text-indent: -36pt;">Additional Mathematics</span></span></u></div>
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<b><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">(A1) Equations and inequalities </span></b></div>
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<b style="text-indent: -24px;"><span style="color: blue;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;"> Conditions for a quadratic equation</span></span></b></div>
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;"><span style="text-indent: -18pt;"> Solving</span><span style="text-indent: -18pt;"> </span><b style="text-indent: -18pt;"><span style="color: blue;">simultaneous equations</span></b><span style="text-indent: -18pt;"> </span><span style="text-indent: -18pt;">in two variables with at least one linear
equation, by substitution</span></span></div>
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<span style="text-indent: -18pt;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;"> Relationships between the <b><span style="color: blue;">roots and coefficients of a quadratic equation</span></b></span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;"><span style="text-indent: -18pt;"> Solving</span><span style="text-indent: -18pt;"> </span><b style="text-indent: -18pt;"><span style="color: blue;">quadratic inequalities</span></b><span style="text-indent: -18pt;">, and representing the solution on the number line</span></span></div>
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<b><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">(A2) Indices and surds</span></b></div>
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;"><b style="text-indent: -24px;"><span style="color: blue;"> Four operations</span></b><span style="text-indent: -24px;"> on indices and surds, including rationalising the denominator</span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;"><b style="text-indent: -24px;"><span style="color: blue;"> Solving equations</span></b><span style="text-indent: -24px;"> involving indices and surds</span></span></div>
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<b><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">(A3) Polynomials and Partial Fractions</span></b></div>
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<span style="text-indent: -24px;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;"> Multiplication and division of polynomials</span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;"><span style="text-indent: -24px;"> Use of </span><b style="text-indent: -24px;"><span style="color: blue;">remainder and factor theorems</span></b></span></div>
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<span style="text-indent: -24px;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;"> Factorisation of polynomials</span></span></div>
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<b style="text-indent: -24px;"><span style="color: blue;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;"> Partial fractions</span></span></b></div>
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<b><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">(A4) Binomial Expansions</span></b></div>
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<b><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">(A5) Power, Exponential, Logarithmic, and Modulus functions</span></b></div>
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;"><b>(G1) </b>Trigonometric functions, identities and equations.</span></div>
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<li><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"><span style="font-size: x-small;">· Six trigonometric functions for angles of any magnitude (in degrees or radians)</span></span></li>
<li><span style="font-size: x-small;"><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">· </span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"><span style="color: blue;">Principal values</span></b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"> of sin</span><span style="font-family: Arial, Helvetica, sans-serif; position: relative; text-indent: -18pt; top: -6pt;">–1</span><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">x, cos</span><span style="font-family: Arial, Helvetica, sans-serif; position: relative; text-indent: -18pt; top: -6pt;">–1</span><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">x, tan</span><span style="font-family: Arial, Helvetica, sans-serif; position: relative; text-indent: -18pt; top: -6pt;">–1</span><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">x</span></span></li>
<li><span style="font-size: x-small;"><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">· Exact values of the trigonometric functions for </span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"><span style="color: blue;">special angles</span></b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">
</span><span style="font-family: Arial, Helvetica, sans-serif; position: relative; text-indent: -18pt; top: 1pt;">(</span><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">30°,45°,60°</span><span style="font-family: Arial, Helvetica, sans-serif; position: relative; text-indent: -18pt; top: 1pt;">) or </span><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">(π/6, π/4, π/3)</span></span></li>
<li><span style="font-size: x-small;"><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">· </span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"><span style="color: blue;">Amplitude, periodicity and symmetries </span></b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">related to the</span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"><span style="color: blue;"> sine and cosine</span></b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"> functions
</span></span></li>
<li><span style="font-size: x-small;"><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">· </span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"><span style="color: blue;">Graphs</span></b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"> of </span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">y </b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"> = </span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">a</b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">sin(</span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">bx</b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">) , </span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">y </b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"> = </span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">a </b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">sin(</span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">x/b + c</b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">), </span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">y </b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"> = </span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">a</b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">cos(</span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">bx</b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">) , </span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">y </b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"> = </span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">a </b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">cos(</span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">x/b + c</b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">) and </span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">y </b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"> = </span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">a</b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">tan(</span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">bx</b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">) , where a is real, b is a positive integer and c is an integer.</span></span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"><span style="font-size: x-small;">· Use of the following</span></span></li>
<li><span style="font-size: x-small;"><span style="font-family: Arial, Helvetica, sans-serif; text-indent: 0px;">∗</span><span style="font-family: Arial, Helvetica, sans-serif; text-indent: 0px;"> (BASIC TRIG RULES)</span></span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: x-small;"> sin A/cos A=tan A,</span></span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: x-small;"> cos A/sin A=cot A, </span></span></li>
<li><span style="font-size: x-small;"><span style="font-family: Arial, Helvetica, sans-serif;"> sin</span><span style="font-family: Arial, Helvetica, sans-serif; position: relative; top: -5pt;">2</span><span style="font-family: Arial, Helvetica, sans-serif;">A+cos</span><span style="font-family: Arial, Helvetica, sans-serif; position: relative; top: -5pt;">2</span><span style="font-family: Arial, Helvetica, sans-serif;">A=1,</span></span></li>
<li><span style="font-size: x-small;"><span style="font-family: Arial, Helvetica, sans-serif;"> sec</span><span style="font-family: Arial, Helvetica, sans-serif; position: relative; top: -5pt;">2</span><span style="font-family: Arial, Helvetica, sans-serif;">A=1+tan</span><span style="font-family: Arial, Helvetica, sans-serif; position: relative; top: -5pt;">2</span><span style="font-family: Arial, Helvetica, sans-serif;">A,</span></span></li>
<li><span style="font-size: x-small;"><span style="font-family: Arial, Helvetica, sans-serif;"> cosec</span><span style="font-family: Arial, Helvetica, sans-serif; position: relative; top: -5pt;">2</span><span style="font-family: Arial, Helvetica, sans-serif;">A =1+cot</span><span style="font-family: Arial, Helvetica, sans-serif; position: relative; top: -5pt;">2</span><span style="font-family: Arial, Helvetica, sans-serif;">A</span></span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: x-small;"> (DOUBLE ANLES)</span></span></li>
<li><span style="font-size: x-small;"><span style="font-family: Arial, Helvetica, sans-serif;"> the expansions of </span><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">sin(A ± B), cos(A ± B) and tan(A ± B)</span></span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;"><span style="font-size: x-small;"> the formulae for sin 2A, cos 2A and tan 2A</span></span></li>
<li><span style="font-size: x-small;"><span style="font-family: Arial, Helvetica, sans-serif;"> (R-FORMULA) - </span><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">the expression for acosu + bsinu in the form </span><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">Rcos(u ± a) or R sin (u ± a)</span></span></li>
<li><span style="font-size: x-small;"><span style="font-family: Arial, Helvetica, sans-serif;"> </span><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">Simplification of trigonometric expressions</span></span></li>
<li><span style="font-size: x-small;"><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">· </span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"><span style="color: blue;">Solution of simple trigonometric equations</span></b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"> in a given interval (excluding
general solution)</span></span></li>
<li><span style="font-size: x-small;"><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;">· </span><b style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"><span style="color: blue;">Proofs</span></b><span style="font-family: Arial, Helvetica, sans-serif; text-indent: -18pt;"> of simple trigonometric identities</span></span></li>
</ul>
<div class="MsoNormal" style="text-indent: 0px;">
<b><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">(G2) Coordinate Geometry</span></b></div>
<div class="MsoNormal" style="text-indent: 0px;">
<span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;"> Condition for two lines to be parallel or perpendicular</span></div>
<div class="MsoNormal" style="text-indent: 0px;">
<b><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">(G2) Linear Law</span></b></div>
<div class="MsoNormal" style="text-indent: 0px;">
</div>
<div class="MsoListParagraphCxSpFirst" style="margin: 0cm 0cm 12pt 18pt; text-indent: -24px;">
<span style="font-size: x-small;"><span style="font-family: Arial, Helvetica, sans-serif; text-indent: 0px;"><span style="color: blue;"><b> </b></span>Transformation of given relationships, including </span><span style="font-family: Arial, Helvetica, sans-serif; text-indent: 0px;">y = ax</span><span style="font-family: Arial, Helvetica, sans-serif; position: relative; text-indent: 0px; top: -6pt;">n </span><span style="font-family: Arial, Helvetica, sans-serif; text-indent: 0px;">and y = kb</span><span style="font-family: Arial, Helvetica, sans-serif; position: relative; text-indent: 0px; top: -6pt;">x</span><span style="font-family: Arial, Helvetica, sans-serif; text-indent: 0px;">, to linear form to determine the unknown constants from a straight line graph</span></span></div>
<br />
<div class="MsoNormal" style="text-indent: 0px;">
<span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;"><br /></span></div>
</div>
</div>
<div style="background-color: white; color: #222222;">
<b><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">Resource and References</span></b></div>
<div style="background-color: white; color: #222222;">
<span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">The following would be useful for revision:</span></div>
<div style="background-color: white; color: #222222;">
<ul>
<li style="margin-left: 15px;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">Maths Workbook</span></li>
<li style="margin-left: 15px;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">Study notes</span></li>
<li style="margin-left: 15px;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">Homework Handouts</span></li>
<li style="margin-left: 15px;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">Exam Prep Booklets (that was given since the beginning of the year)</span></li>
<li style="margin-left: 15px;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">Ace Learning Portal - where they could attempt practices that are auto-mark</span></li>
<li style="margin-left: 15px;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">Past GCEO EM and AM questions (students were recommended to purchase these at the beginning of the year)</span></li>
</ul>
</div>
<div style="background-color: white; color: #222222;">
<div>
<b style="background-color: yellow;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;"><br /></span></b></div>
<div>
<b style="background-color: yellow;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">(4) General Consultation and Timed-trial during the school holidays</span></b></div>
</div>
<div style="background-color: white; color: #222222;">
<span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;"><br /></span></div>
<span style="background-color: white;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;"><span style="color: #222222;">During the school holidays, there would be a timed-trial on </span><b><span style="color: red;">Monday 9 September 2013</span></b><span style="color: #222222;"> (Monday). The focus would be on Additional Mathematics and students are strongly encouraged to attend.</span></span></span><br />
<div>
<span style="background-color: white; color: #222222;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: x-small;">Duration: 0800 - 1030 (2 hours 30 minutes) </span></span></div>
Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-7991892050140229718.post-10327539600335181282013-08-31T04:04:00.001-07:002013-08-31T06:18:31.175-07:00Mathematics Performance Task 2 <div class="separator" style="clear: both; text-align: center;">
<b><span style="font-size: large;">Due Term 4 Week 1 (first Mathematics Lesson)</span></b></div>
<div class="separator" style="clear: both; text-align: center;">
<i>the file could be downloaded from google site.</i></div>
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Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-7991892050140229718.post-50067301800320164112013-08-28T21:53:00.002-07:002013-08-31T06:11:35.470-07:00Essential GDC Skills<!--[if gte mso 9]><xml>
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<b><span style="font-family: "Times New Roman";">Essential GDC Skills<o:p></o:p></span></b></div>
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<br /></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman";">View each video
carefully and learn these fundamental GDC skills.<o:p></o:p></span></div>
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<br /></div>
<div class="MsoNormal">
<b><span style="font-family: "Times New Roman";">1. Basic Graphing Controls<o:p></o:p></span></b></div>
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<span style="font-family: "Times New Roman";">a. Zoom Options<o:p></o:p></span></div>
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<a href="http://www.youtube.com/watch?v=r7DWbhWd9zE&list=PLB1A524363687A860"><span style="font-family: "Times New Roman";">http://www.youtube.com/watch?v=r7DWbhWd9zE&list=PLB1A524363687A860</span></a><span style="font-family: "Times New Roman";"><o:p></o:p></span></div>
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<span style="font-family: "Times New Roman";">b. Setting the
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<span style="font-family: "Times New Roman";"><a href="http://www.youtube.com/watch?v=a_uJpI6LXr4">http://www.youtube.com/watch?v=a_uJpI6LXr4</a></span><span style="font-family: "Times New Roman";"><o:p></o:p></span><br />
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<b><span style="font-family: "Times New Roman";">2. Graphing Basics<o:p></o:p></span></b></div>
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<br /></div>
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<span style="font-family: "Times New Roman";">a. Graph a line
and find the table of values:<o:p></o:p></span></div>
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<a href="http://www.youtube.com/watch?v=3WctC2xCnI0"><span style="font-family: "Times New Roman";">http://www.youtube.com/watch?v=3WctC2xCnI0</span></a><span style="font-family: "Times New Roman";"><o:p></o:p></span></div>
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<span style="font-family: "Times New Roman";">b. Finding
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<br /></div>
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<span style="font-family: "Times New Roman";">c. Finding
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<a href="http://www.youtube.com/watch?v=M-1QUYQbYHM"><span style="font-family: "Times New Roman";">http://www.youtube.com/watch?v=M-1QUYQbYHM</span></a><span style="font-family: "Times New Roman";"><o:p></o:p></span></div>
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<span style="font-family: "Times New Roman";">d. Finding roots
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<b><span style="font-family: "Times New Roman";">3. PlySmlt2<o:p></o:p></span></b></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman";">a. Using
PlySmlt2 for Solving Quadratic Equations<o:p></o:p></span></div>
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<a href="http://www.youtube.com/watch?v=NBRzvsJ6ros"><span style="font-family: "Times New Roman";">http://www.youtube.com/watch?v=NBRzvsJ6ros</span></a><span style="font-family: "Times New Roman";"><o:p></o:p></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman";">b. Using
PlySmlt2 to Solve a System of Equations<o:p></o:p></span></div>
<div class="MsoNormal">
<a href="http://www.youtube.com/watch?v=Dyox4aNR0Zc"><span style="font-family: "Times New Roman";">http://www.youtube.com/watch?v=Dyox4aNR0Zc</span></a><span style="font-family: "Times New Roman";"><o:p></o:p></span></div>
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<br /></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman";">c. Using
PlySmlt2 to Solve Polynomial Equations<o:p></o:p></span></div>
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<span style="font-family: "Times New Roman";"><a href="http://www.youtube.com/watch?v=3CoNcxnVbtY">http://www.youtube.com/watch?v=3CoNcxnVbtY</a></span><span style="font-family: "Times New Roman";"><o:p></o:p></span></div>
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<br /></div>
<div class="MsoNormal">
<br /></div>
<!--EndFragment-->
<iframe allowfullscreen="" frameborder="0" height="315" src="//www.youtube.com/embed/3CoNcxnVbtY" width="560"></iframe>Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-7991892050140229718.post-36216224292493011722013-08-17T04:59:00.000-07:002013-08-17T04:59:01.318-07:00TRIGONOMETRY : Compound and Double Angles<div class="separator" style="clear: both; text-align: center;">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1mzqRpuFMBd1W-Z3M1Bz5dlQQ0Szwbfx4fK2tWb6mAwmWuKuO_fSi9I9R45j0kq2xmjG5hyphenhyphen6VWvzVqZD9uuz0m5-d-Tj5zB07lq86UNFOlnLvxDuYqFM-cP432z07RvPbrDoMhi6b76XK/s1600/Screen+Shot+2013-08-17+at+7.55.53+PM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="574" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1mzqRpuFMBd1W-Z3M1Bz5dlQQ0Szwbfx4fK2tWb6mAwmWuKuO_fSi9I9R45j0kq2xmjG5hyphenhyphen6VWvzVqZD9uuz0m5-d-Tj5zB07lq86UNFOlnLvxDuYqFM-cP432z07RvPbrDoMhi6b76XK/s640/Screen+Shot+2013-08-17+at+7.55.53+PM.png" width="640" /></a></div>
<br />Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-7991892050140229718.post-80630716569425970092013-08-04T21:44:00.002-07:002013-08-04T21:44:43.765-07:00TI84 Wave Generator<br />
<div style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; color: #333333; font-family: Arial, Verdana, Helvetica, sans-serif; font-size: 14px; line-height: 22px; margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">
This activity is walks you through the steps to perform sine regression for a randomly generated data set using the TI-84.</div>
<h2 style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; clear: both; color: #1a1c61; font-family: 'Open Sans', 'Century Gothic', 'Trebuchet MS', 'Arial Narrow', Arial, sans-serif; font-size: 30px; font-weight: normal; letter-spacing: -2px; line-height: 22px; margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 20px; padding-bottom: 10px; padding-left: 10px; padding-right: 0px; padding-top: 10px; vertical-align: baseline;">
Step 1: Get some data.</h2>
<ul style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; color: #333333; font-family: Arial, Verdana, Helvetica, sans-serif; font-size: 14px; line-height: 22px; list-style-image: initial; list-style-position: initial; list-style-type: square; margin-bottom: 10px; margin-left: 1.5em; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">
<li style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">Go to the <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;"><a href="http://faculty.tamucc.edu/jchampion/randomized-wave-data-generator/" target="_blank">Randomized Wave Data Generator</a></strong> and use the form to get some randomly-generated data (check the boxes for more interesting data).</li>
<li style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">Your data should be different from every other data set on earth, so copy and paste it to a (spreadsheet or word-processor) file for your later use.</li>
</ul>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSkkNnB-EyMpnZdcjm33Z0yZp6heDZx25JSCqPWKA5HKZdzUYtEKUFqPpzy7D1Jxr4ikN_8YQI9dBZa1iFwAmg9M5sFV5OYo46MMLmy6MEKNva3lWy2DNpkehUzT8h653GNnPw2XPfR4g/s1600/Screen+shot+2013-07-28+at+PM+02.58.51.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="126" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSkkNnB-EyMpnZdcjm33Z0yZp6heDZx25JSCqPWKA5HKZdzUYtEKUFqPpzy7D1Jxr4ikN_8YQI9dBZa1iFwAmg9M5sFV5OYo46MMLmy6MEKNva3lWy2DNpkehUzT8h653GNnPw2XPfR4g/s320/Screen+shot+2013-07-28+at+PM+02.58.51.png" width="320" /></a></div>
<div>
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<h2 style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; clear: both; color: #1a1c61; font-family: 'Open Sans', 'Century Gothic', 'Trebuchet MS', 'Arial Narrow', Arial, sans-serif; font-size: 30px; font-weight: normal; letter-spacing: -2px; line-height: 22px; margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 20px; padding-bottom: 10px; padding-left: 10px; padding-right: 0px; padding-top: 10px; vertical-align: baseline;">
<span style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">Step 2: Enter the Data into your Calculator.</span></h2>
<ol style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; color: #333333; font-family: Arial, Verdana, Helvetica, sans-serif; font-size: 14px; line-height: 22px; list-style-image: initial; list-style-position: initial; list-style-type: decimal; margin-bottom: 10px; margin-left: 1.5em; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">
<li style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">Press <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">Y=</strong> and clear the Y1 function.</li>
<li style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">Press <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">STATPLOT</strong> (2nd followed by Y=) and choose<strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;"> Plot1</strong>.</li>
<li style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">Under Plot1, select <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">On</strong> (press ENTER), after <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">Type</strong> select the drawing of disconnected dots, and make sure you have<strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;"> Xlist: L1</strong>(2nd followed by 1) and <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">Ylist: L2</strong> (2nd followed by 2).</li>
<li style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">Press <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">STAT</strong>. With <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">EDIT</strong> highlighted, select <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">1:Edit…</strong></li>
<li style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">In the table that appears, under <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">L1</strong> type the x values and under<strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;"> L2</strong> type the values of y. <span style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: underline; vertical-align: baseline;">Make sure your L1 and L2 lists have the same length. (key in the data obtained from the Randomised Wave Generator)</span></li>
<li style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">Press <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">ZOOM</strong> and choose option <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">9:ZoomStat</strong> to look at a scatter plot of your data.</li>
</ol>
<h2 style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; clear: both; color: #1a1c61; font-family: 'Open Sans', 'Century Gothic', 'Trebuchet MS', 'Arial Narrow', Arial, sans-serif; font-size: 30px; font-weight: normal; letter-spacing: -2px; line-height: 22px; margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 20px; padding-bottom: 10px; padding-left: 10px; padding-right: 0px; padding-top: 10px; vertical-align: baseline;">
Step 3: Find the Sine Wave of Best Fit for the Data.</h2>
<ol style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; color: #333333; font-family: Arial, Verdana, Helvetica, sans-serif; font-size: 14px; line-height: 22px; list-style-image: initial; list-style-position: initial; list-style-type: decimal; margin-bottom: 10px; margin-left: 1.5em; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">
<li style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">Press <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">STAT</strong>. Press the right arrow key to highlight <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">CALC</strong>. Then scroll down to select <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">C:SinReg </strong>and press<strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">ENTER </strong><span style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: underline; vertical-align: baseline;">ONCE</span><strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">.</strong></li>
<li style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">In the SinReg screen, choose Iterations:3 Xlist:L1, Ylist:L2 and Store RegEq: Y1 (press VARS, then select Y-VARS , then select FUNCTION, and then select Y1). Then highlight Calculate and press <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">ENTER</strong> <span style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: underline; vertical-align: baseline;">ONCE</span>.</li>
<li style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">The calculator should now display the values for <span class="MathJax_Preview" style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; color: #888888; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-1-Frame" role="textbox" style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; direction: ltr; display: inline; float: none; font-size: 14px; font-style: normal; font-weight: normal; letter-spacing: normal; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-align: left; text-indent: 0px; text-transform: none; vertical-align: baseline; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; max-height: 5000em; max-width: 5000em; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none; vertical-align: 0px; white-space: nowrap !important;"><span class="math" id="MathJax-Span-1" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px; width: 0.661em;"><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; font-size: 17px; height: 0px; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: relative; text-decoration: none; vertical-align: 0px; width: 0.536em;"><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; clip: rect(1.94em 1000em 2.748em -0.503em); display: inline; left: 0em; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: absolute; text-decoration: none; top: -2.56em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-2" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;"><span class="mi" id="MathJax-Span-3" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Math; font-style: italic; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">a</span></span><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; height: 2.56em; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px; width: 0px;"></span></span></span><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-color: initial; border-left-style: solid; border-left-width: 0em; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; height: 0.684em; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; overflow-x: hidden; overflow-y: hidden; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: -0.083em; width: 0px;"></span></span></nobr></span>, <span class="MathJax_Preview" style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; color: #888888; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-2-Frame" role="textbox" style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; direction: ltr; display: inline; float: none; font-size: 14px; font-style: normal; font-weight: normal; letter-spacing: normal; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-align: left; text-indent: 0px; text-transform: none; vertical-align: baseline; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; max-height: 5000em; max-width: 5000em; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none; vertical-align: 0px; white-space: nowrap !important;"><span class="math" id="MathJax-Span-4" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px; width: 0.518em;"><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; font-size: 17px; height: 0px; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: relative; text-decoration: none; vertical-align: 0px; width: 0.417em;"><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; clip: rect(1.687em 1000em 2.749em -0.496em); display: inline; left: 0em; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: absolute; text-decoration: none; top: -2.56em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-5" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;"><span class="mi" id="MathJax-Span-6" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Math; font-style: italic; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">b</span></span><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; height: 2.56em; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px; width: 0px;"></span></span></span><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-color: initial; border-left-style: solid; border-left-width: 0em; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; height: 0.989em; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; overflow-x: hidden; overflow-y: hidden; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: -0.085em; width: 0px;"></span></span></nobr></span>, <span class="MathJax_Preview" style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; color: #888888; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-3-Frame" role="textbox" style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; direction: ltr; display: inline; float: none; font-size: 14px; font-style: normal; font-weight: normal; letter-spacing: normal; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-align: left; text-indent: 0px; text-transform: none; vertical-align: baseline; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; max-height: 5000em; max-width: 5000em; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none; vertical-align: 0px; white-space: nowrap !important;"><span class="math" id="MathJax-Span-7" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px; width: 0.518em;"><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; font-size: 17px; height: 0px; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: relative; text-decoration: none; vertical-align: 0px; width: 0.417em;"><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; clip: rect(1.939em 1000em 2.749em -0.502em); display: inline; left: 0em; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: absolute; text-decoration: none; top: -2.56em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-8" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;"><span class="mi" id="MathJax-Span-9" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Math; font-style: italic; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">c</span></span><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; height: 2.56em; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px; width: 0px;"></span></span></span><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-color: initial; border-left-style: solid; border-left-width: 0em; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; height: 0.686em; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; overflow-x: hidden; overflow-y: hidden; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: -0.085em; width: 0px;"></span></span></nobr></span>, and <span class="MathJax_Preview" style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; color: #888888; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-4-Frame" role="textbox" style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; direction: ltr; display: inline; float: none; font-size: 14px; font-style: normal; font-weight: normal; letter-spacing: normal; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-align: left; text-indent: 0px; text-transform: none; vertical-align: baseline; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; max-height: 5000em; max-width: 5000em; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none; vertical-align: 0px; white-space: nowrap !important;"><span class="math" id="MathJax-Span-10" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px; width: 0.661em;"><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; font-size: 17px; height: 0px; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: relative; text-decoration: none; vertical-align: 0px; width: 0.536em;"><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; clip: rect(1.687em 1000em 2.748em -0.503em); display: inline; left: 0em; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: absolute; text-decoration: none; top: -2.56em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-11" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;"><span class="mi" id="MathJax-Span-12" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Math; font-style: italic; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">d<span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; height: 1px; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; overflow-x: hidden; overflow-y: hidden; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px; width: 0.003em;"></span></span></span><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; height: 2.56em; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px; width: 0px;"></span></span></span><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-color: initial; border-left-style: solid; border-left-width: 0em; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; height: 0.988em; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; overflow-x: hidden; overflow-y: hidden; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: -0.083em; width: 0px;"></span></span></nobr></span> in the function <span class="MathJax_Preview" style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; color: #888888; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-5-Frame" role="textbox" style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; direction: ltr; display: inline; float: none; font-size: 14px; font-style: normal; font-weight: normal; letter-spacing: normal; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-align: left; text-indent: 0px; text-transform: none; vertical-align: baseline; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; max-height: 5000em; max-width: 5000em; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none; vertical-align: 0px; white-space: nowrap !important;"><span class="math" id="MathJax-Span-13" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px; width: 12.304em;"><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; font-size: 17px; height: 0px; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: relative; text-decoration: none; vertical-align: 0px; width: 10.238em;"><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; clip: rect(1.869em 1000em 3.226em -0.481em); display: inline; left: 0em; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: absolute; text-decoration: none; top: -2.798em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-14" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;"><span class="mi" id="MathJax-Span-15" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Math; font-style: italic; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">f<span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; height: 1px; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; overflow-x: hidden; overflow-y: hidden; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px; width: 0.06em;"></span></span><span class="mo" id="MathJax-Span-16" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">(</span><span class="mi" id="MathJax-Span-17" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Math; font-style: italic; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">x</span><span class="mo" id="MathJax-Span-18" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">)</span><span class="mo" id="MathJax-Span-19" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0.278em; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">=</span><span class="mi" id="MathJax-Span-20" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Math; font-style: italic; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0.278em; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">a</span><span class="mi" id="MathJax-Span-21" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Math; font-style: italic; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">s</span><span class="mi" id="MathJax-Span-22" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Math; font-style: italic; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">i</span><span class="mi" id="MathJax-Span-23" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Math; font-style: italic; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">n</span><span class="mo" id="MathJax-Span-24" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">(</span><span class="mi" id="MathJax-Span-25" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Math; font-style: italic; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">b</span><span class="mi" id="MathJax-Span-26" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Math; font-style: italic; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">x</span><span class="mo" id="MathJax-Span-27" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0.222em; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">+</span><span class="mi" id="MathJax-Span-28" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Math; font-style: italic; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0.222em; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">c</span><span class="mo" id="MathJax-Span-29" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">)</span><span class="mo" id="MathJax-Span-30" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0.222em; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">+</span><span class="mi" id="MathJax-Span-31" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Math; font-style: italic; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0.222em; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">d<span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; height: 1px; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; overflow-x: hidden; overflow-y: hidden; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px; width: 0.003em;"></span></span></span><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; height: 2.798em; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px; width: 0px;"></span></span></span><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-color: initial; border-left-style: solid; border-left-width: 0em; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; height: 1.343em; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; overflow-x: hidden; overflow-y: hidden; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: -0.371em; width: 0px;"></span></span></nobr></span>that best fits the given data set.</li>
<li style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">Press GRAPH to see the sine regression function plotted along with your scatter plot and press Y1 to see the equation of your wave.</li>
</ol>
<div>
<h2 style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; clear: both; color: #1a1c61; font-family: 'Open Sans', 'Century Gothic', 'Trebuchet MS', 'Arial Narrow', Arial, sans-serif; font-size: 30px; font-weight: normal; letter-spacing: -2px; line-height: 22px; margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 20px; padding-bottom: 10px; padding-left: 10px; padding-right: 0px; padding-top: 10px; vertical-align: baseline;">
<span class="Apple-style-span" style="color: red;">Task: in sub groups of 3s</span></h2>
</div>
<div>
<ol style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; color: #333333; font-family: Arial, Verdana, Helvetica, sans-serif; font-size: 14px; line-height: 22px; list-style-image: initial; list-style-position: initial; list-style-type: decimal; margin-bottom: 10px; margin-left: 1.5em; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">
<li style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">Using the <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;"><a href="http://faculty.tamucc.edu/jchampion/randomized-wave-data-generator/" target="_blank">Randomized Wave Data Generator</a></strong> generate a (1) Set of Data.</li>
<li style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">Identify the best fit function <span aria-readonly="true" class="MathJax" id="MathJax-Element-5-Frame" role="textbox" style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; direction: ltr; display: inline; float: none; font-size: 14px; font-style: normal; font-weight: normal; letter-spacing: normal; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-align: left; text-indent: 0px; text-transform: none; vertical-align: baseline; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; max-height: 5000em; max-width: 5000em; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none; vertical-align: 0px; white-space: nowrap !important;"><span class="math" id="MathJax-Span-13" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px; width: 12.304em;"><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; font-size: 17px; height: 0px; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: relative; text-decoration: none; vertical-align: 0px; width: 10.238em;"><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; clip: rect(1.869em 1000em 3.226em -0.481em); display: inline; left: 0em; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: absolute; text-decoration: none; top: -2.798em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-14" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;"><span class="mi" id="MathJax-Span-15" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Math; font-style: italic; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">f<span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; height: 1px; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; overflow-x: hidden; overflow-y: hidden; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px; width: 0.06em;"></span></span><span class="mo" id="MathJax-Span-16" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">(</span><span class="mi" id="MathJax-Span-17" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Math; font-style: italic; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">x</span><span class="mo" id="MathJax-Span-18" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">)</span><span class="mo" id="MathJax-Span-19" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0.278em; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">=</span><span class="mi" id="MathJax-Span-20" style="-webkit-transition-delay: initial; 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background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Math; font-style: italic; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">s</span><span class="mi" id="MathJax-Span-22" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Math; font-style: italic; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">i</span><span class="mi" id="MathJax-Span-23" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; 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display: inline; font-family: MathJax_Math; font-style: italic; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">b</span><span class="mi" id="MathJax-Span-26" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Math; font-style: italic; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">x</span><span class="mo" id="MathJax-Span-27" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0.222em; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">+</span><span class="mi" id="MathJax-Span-28" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Math; font-style: italic; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0.222em; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">c</span><span class="mo" id="MathJax-Span-29" style="-webkit-transition-delay: initial; 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display: inline-block; height: 1.343em; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; overflow-x: hidden; overflow-y: hidden; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: -0.371em; width: 0px;"></span></span></nobr></span>that best fits the given data set</li>
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border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Math; font-style: italic; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">x</span><span class="mo" id="MathJax-Span-29" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">) as a bench mark points. Your explanation should be as follows</span></span></span></span></span></nobr></span></li>
</ol>
<span class="Apple-style-span" style="white-space: nowrap;"></span><br />
<ul><span class="Apple-style-span" style="white-space: nowrap;">
<li>Increase in amplitude by a</li>
<li>period change by ....</li>
<li>vertical shift by .... </li>
</span></ul>
<span class="Apple-style-span" style="white-space: nowrap;">
</span></div>
Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-7991892050140229718.post-18602191419486027592013-08-04T21:44:00.000-07:002013-08-04T21:44:14.187-07:00Trigonometry T1-84 (Activity)<br />
<div style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; color: #333333; font-family: Arial, Verdana, Helvetica, sans-serif; font-size: 14px; line-height: 22px; margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">
his activity is walks you through the steps to perform sine regression for a randomly generated data set using the TI-84.</div>
<h2 style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; clear: both; color: #1a1c61; font-family: 'Open Sans', 'Century Gothic', 'Trebuchet MS', 'Arial Narrow', Arial, sans-serif; font-size: 30px; font-weight: normal; letter-spacing: -2px; line-height: 22px; margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 20px; padding-bottom: 10px; padding-left: 10px; padding-right: 0px; padding-top: 10px; vertical-align: baseline;">
Step 1: Get a TI-84 Graphing Calculator (or similar).</h2>
<ul style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; color: #333333; font-family: Arial, Verdana, Helvetica, sans-serif; font-size: 14px; line-height: 22px; list-style-image: initial; list-style-position: initial; list-style-type: square; margin-bottom: 10px; margin-left: 1.5em; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">
<li style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">Don’t have one? If you use Windows, you can download the attached <a href="http://faculty.tamucc.edu/jchampion/wp-content/uploads/emulator84.zip" style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; color: #005091; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none; vertical-align: baseline;">Emulator (ZIP file)</a>, extract the Zip folder, and run the Wabbitemu.exe file. Load the rom file when prompted and just choose the View > Enable skin option to work with your virtual calculator.</li>
</ul>
<h2 style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; clear: both; color: #1a1c61; font-family: 'Open Sans', 'Century Gothic', 'Trebuchet MS', 'Arial Narrow', Arial, sans-serif; font-size: 30px; font-weight: normal; letter-spacing: -2px; line-height: 22px; margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 20px; padding-bottom: 10px; padding-left: 10px; padding-right: 0px; padding-top: 10px; vertical-align: baseline;">
Step 2: Get some data.</h2>
<ul style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; color: #333333; font-family: Arial, Verdana, Helvetica, sans-serif; font-size: 14px; line-height: 22px; list-style-image: initial; list-style-position: initial; list-style-type: square; margin-bottom: 10px; margin-left: 1.5em; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">
<li style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">Go to the <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;"><a href="http://faculty.tamucc.edu/jchampion/2011/randomized-wave-data-generator/" style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; color: #005091; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none; vertical-align: baseline;">Randomized Wave Data Generator</a></strong> and use the form to get some randomly-generated data (check the boxes for more interesting data).</li>
<li style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">Your data should be different from every other data set on earth, so copy and paste it to a (spreadsheet or word-processor) file for your later use.</li>
</ul>
<h2 style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; clear: both; color: #1a1c61; font-family: 'Open Sans', 'Century Gothic', 'Trebuchet MS', 'Arial Narrow', Arial, sans-serif; font-size: 30px; font-weight: normal; letter-spacing: -2px; line-height: 22px; margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 20px; padding-bottom: 10px; padding-left: 10px; padding-right: 0px; padding-top: 10px; vertical-align: baseline;">
<span style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">Step 3: Enter the Data into your Calculator.</span></h2>
<ol style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; color: #333333; font-family: Arial, Verdana, Helvetica, sans-serif; font-size: 14px; line-height: 22px; list-style-image: initial; list-style-position: initial; list-style-type: decimal; margin-bottom: 10px; margin-left: 1.5em; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">
<li style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">Press <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">Y=</strong> and clear the Y1 function.</li>
<li style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">Press <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">STATPLOT</strong> (2nd followed by Y=) and choose<strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;"> Plot1</strong>.</li>
<li style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">Under Plot1, select <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">On</strong> (press ENTER), after <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">Type</strong> select the drawing of disconnected dots, and make sure you have<strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;"> Xlist: L1</strong>(2nd followed by 1) and <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">Ylist: L2</strong> (2nd followed by 2).</li>
<li style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">Press <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">STAT</strong>. With <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">EDIT</strong> highlighted, select <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">1:Edit…</strong></li>
<li style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">In the table that appears, under <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">L1</strong> type the x values and under<strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;"> L2</strong> type the values of y. <span style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: underline; vertical-align: baseline;">Make sure your L1 and L2 lists have the same length.</span></li>
<li style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">Press <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">ZOOM</strong> and choose option <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">9:ZoomStat</strong> to look at a scatter plot of your data.</li>
</ol>
<h2 style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; clear: both; color: #1a1c61; font-family: 'Open Sans', 'Century Gothic', 'Trebuchet MS', 'Arial Narrow', Arial, sans-serif; font-size: 30px; font-weight: normal; letter-spacing: -2px; line-height: 22px; margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 20px; padding-bottom: 10px; padding-left: 10px; padding-right: 0px; padding-top: 10px; vertical-align: baseline;">
Step 4: Find the Sine Wave of Best Fit for the Data.</h2>
<ol style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; color: #333333; font-family: Arial, Verdana, Helvetica, sans-serif; font-size: 14px; line-height: 22px; list-style-image: initial; list-style-position: initial; list-style-type: decimal; margin-bottom: 10px; margin-left: 1.5em; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">
<li style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">Press <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">STAT</strong>. Press the right arrow key to highlight <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">CALC</strong>. Then scroll down to select <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">C:SinReg </strong>and press<strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">ENTER </strong><span style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: underline; vertical-align: baseline;">ONCE</span><strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">.</strong></li>
<li style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;"><strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">[Older Versions]</strong> After the word SinReg, which should now be on the screen, enter <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">L1</strong>(2nd followed by 1), then type a <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">comma</strong> (just above the 7 key), then enter <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">L2</strong> (2nd followed by 2), then type another <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">comma</strong>, and then enter <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">Y1</strong> (press VARS, then select Y-VARS , then select FUNCTION, and then select Y1) . Your screen should now read <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">SinReg L1, L2, Y1</strong>. Then press <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">ENTER</strong> <span style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: underline; vertical-align: baseline;">ONCE</span>.</li>
<li style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;"><strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">[Newer Versions]</strong> In the SinReg screen, choose Iterations:3 Xlist:L1, Ylist:L2 and Store RegEq: Y1 (press VARS, then select Y-VARS , then select FUNCTION, and then select Y1). Then highlight Calculate and press <strong style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; font-weight: bold; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">ENTER</strong> <span style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: underline; vertical-align: baseline;">ONCE</span>.</li>
<li style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">The calculator should now display the values for <span class="MathJax_Preview" style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; color: #888888; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-1-Frame" role="textbox" style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; direction: ltr; display: inline; float: none; font-size: 14px; font-style: normal; font-weight: normal; letter-spacing: normal; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-align: left; text-indent: 0px; text-transform: none; vertical-align: baseline; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; max-height: 5000em; max-width: 5000em; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none; vertical-align: 0px; white-space: nowrap !important;"><span class="math" id="MathJax-Span-1" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px; width: 0.661em;"><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; font-size: 17px; height: 0px; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: relative; text-decoration: none; vertical-align: 0px; width: 0.536em;"><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; clip: rect(1.94em 1000em 2.748em -0.503em); display: inline; left: 0em; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: absolute; text-decoration: none; top: -2.56em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-2" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;"><span class="mi" id="MathJax-Span-3" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Math; font-style: italic; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">a</span></span><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; height: 2.56em; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px; width: 0px;"></span></span></span><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-color: initial; border-left-style: solid; border-left-width: 0em; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; height: 0.684em; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; overflow-x: hidden; overflow-y: hidden; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: -0.083em; width: 0px;"></span></span></nobr></span>, <span class="MathJax_Preview" style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; color: #888888; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-2-Frame" role="textbox" style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; direction: ltr; display: inline; float: none; font-size: 14px; font-style: normal; font-weight: normal; letter-spacing: normal; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-align: left; text-indent: 0px; text-transform: none; vertical-align: baseline; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; max-height: 5000em; max-width: 5000em; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none; vertical-align: 0px; white-space: nowrap !important;"><span class="math" id="MathJax-Span-4" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px; width: 0.518em;"><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; font-size: 17px; height: 0px; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: relative; text-decoration: none; vertical-align: 0px; width: 0.417em;"><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; clip: rect(1.687em 1000em 2.749em -0.496em); display: inline; left: 0em; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: absolute; text-decoration: none; top: -2.56em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-5" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;"><span class="mi" id="MathJax-Span-6" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Math; font-style: italic; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">b</span></span><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; height: 2.56em; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px; width: 0px;"></span></span></span><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-color: initial; border-left-style: solid; border-left-width: 0em; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; height: 0.989em; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; overflow-x: hidden; overflow-y: hidden; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: -0.085em; width: 0px;"></span></span></nobr></span>, <span class="MathJax_Preview" style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; color: #888888; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-3-Frame" role="textbox" style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; direction: ltr; display: inline; float: none; font-size: 14px; font-style: normal; font-weight: normal; letter-spacing: normal; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-align: left; text-indent: 0px; text-transform: none; vertical-align: baseline; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; max-height: 5000em; max-width: 5000em; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none; vertical-align: 0px; white-space: nowrap !important;"><span class="math" id="MathJax-Span-7" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px; width: 0.518em;"><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; font-size: 17px; height: 0px; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: relative; text-decoration: none; vertical-align: 0px; width: 0.417em;"><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; clip: rect(1.939em 1000em 2.749em -0.502em); display: inline; left: 0em; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: absolute; text-decoration: none; top: -2.56em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-8" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;"><span class="mi" id="MathJax-Span-9" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Math; font-style: italic; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">c</span></span><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; height: 2.56em; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px; width: 0px;"></span></span></span><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-color: initial; border-left-style: solid; border-left-width: 0em; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; height: 0.686em; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; overflow-x: hidden; overflow-y: hidden; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: -0.085em; width: 0px;"></span></span></nobr></span>, and <span class="MathJax_Preview" style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; color: #888888; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-4-Frame" role="textbox" style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; direction: ltr; display: inline; float: none; font-size: 14px; font-style: normal; font-weight: normal; letter-spacing: normal; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-align: left; text-indent: 0px; text-transform: none; vertical-align: baseline; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; max-height: 5000em; max-width: 5000em; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none; vertical-align: 0px; white-space: nowrap !important;"><span class="math" id="MathJax-Span-10" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px; width: 0.661em;"><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; font-size: 17px; height: 0px; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: relative; text-decoration: none; vertical-align: 0px; width: 0.536em;"><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; clip: rect(1.687em 1000em 2.748em -0.503em); display: inline; left: 0em; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: absolute; text-decoration: none; top: -2.56em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-11" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;"><span class="mi" id="MathJax-Span-12" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Math; font-style: italic; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">d<span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; height: 1px; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; overflow-x: hidden; overflow-y: hidden; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px; width: 0.003em;"></span></span></span><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; height: 2.56em; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px; width: 0px;"></span></span></span><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-color: initial; border-left-style: solid; border-left-width: 0em; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; height: 0.988em; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; overflow-x: hidden; overflow-y: hidden; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: -0.083em; width: 0px;"></span></span></nobr></span> in the function <span class="MathJax_Preview" style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; color: #888888; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;"></span><span aria-readonly="true" class="MathJax" id="MathJax-Element-5-Frame" role="textbox" style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; direction: ltr; display: inline; float: none; font-size: 14px; font-style: normal; font-weight: normal; letter-spacing: normal; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-align: left; text-indent: 0px; text-transform: none; vertical-align: baseline; white-space: nowrap; word-spacing: normal; word-wrap: normal;"><nobr style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; max-height: 5000em; max-width: 5000em; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none; vertical-align: 0px; white-space: nowrap !important;"><span class="math" id="MathJax-Span-13" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px; width: 12.304em;"><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; font-size: 17px; height: 0px; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: relative; text-decoration: none; vertical-align: 0px; width: 10.238em;"><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; clip: rect(1.869em 1000em 3.226em -0.481em); display: inline; left: 0em; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: absolute; text-decoration: none; top: -2.798em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-14" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; 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height: 1px; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; overflow-x: hidden; overflow-y: hidden; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px; width: 0.06em;"></span></span><span class="mo" id="MathJax-Span-16" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin-bottom: 0px; 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padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">x</span><span class="mo" id="MathJax-Span-18" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">)</span><span class="mo" id="MathJax-Span-19" style="-webkit-transition-delay: initial; 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margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">b</span><span class="mi" id="MathJax-Span-26" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Math; font-style: italic; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">x</span><span class="mo" id="MathJax-Span-27" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Main; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0.222em; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">+</span><span class="mi" id="MathJax-Span-28" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Math; font-style: italic; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0.222em; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">c</span><span class="mo" id="MathJax-Span-29" style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; 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border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline; font-family: MathJax_Math; font-style: italic; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0.222em; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px;">d<span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; height: 1px; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; overflow-x: hidden; overflow-y: hidden; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px; width: 0.003em;"></span></span></span><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; height: 2.798em; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: 0px; width: 0px;"></span></span></span><span style="-webkit-transition-delay: initial; -webkit-transition-duration: initial; -webkit-transition-property: none; -webkit-transition-timing-function: initial; background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-color: initial; border-left-color: initial; border-left-style: solid; border-left-width: 0em; border-right-width: 0px; border-style: initial; border-style: initial; border-top-width: 0px; display: inline-block; height: 1.343em; line-height: normal; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; overflow-x: hidden; overflow-y: hidden; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; position: static; text-decoration: none; vertical-align: -0.371em; width: 0px;"></span></span></nobr></span>that best fits the given data set.</li>
<li style="background-attachment: initial; background-clip: initial; background-color: transparent; background-image: initial; background-origin: initial; background-position: initial initial; background-repeat: initial initial; border-bottom-width: 0px; border-color: initial; border-left-width: 0px; border-right-width: 0px; border-style: initial; border-top-width: 0px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; vertical-align: baseline;">Press GRAPH to see the sine regression function plotted along with your scatter plot and press Y1 to see the equation of your wave.</li>
</ol>
Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-7991892050140229718.post-40656274566095051762013-07-29T19:13:00.002-07:002013-07-29T19:13:19.316-07:00summary for July 30 's lessonTRIGO<br />
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1.Definition of trigonometry, identify tan, cot, sin, cos, cosec, sec in a given triangle.</div>
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2.Unit circle and "CAST" rule , memorize the symbol and values of trigonometry in different angles.</div>
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3.Different trigonometry rules: sine rule, cosine rule, area formula, special relationship and how to transfer in different trigo values.</div>
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4.Memorize values of special angles.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnKbAxNT43Rb-eTL9VWn3DzM1JNv2zg0BDjES1SzA0ETG3vMWL_-1Pb-R0qHluPV5Bt64seWM4a24Agp5HBprPrm8DYST0LDaJZPiMU5Vcx9lA6ase8IdM75XGyYoRoZMYOst0Qh6PwWs/s1600/IMG_20130730_100806.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="360" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnKbAxNT43Rb-eTL9VWn3DzM1JNv2zg0BDjES1SzA0ETG3vMWL_-1Pb-R0qHluPV5Bt64seWM4a24Agp5HBprPrm8DYST0LDaJZPiMU5Vcx9lA6ase8IdM75XGyYoRoZMYOst0Qh6PwWs/s640/IMG_20130730_100806.jpg" width="640" /></a></div>
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Anonymoushttp://www.blogger.com/profile/10616114183349270022noreply@blogger.com0tag:blogger.com,1999:blog-7991892050140229718.post-80643567476305716482013-07-25T07:08:00.003-07:002013-07-25T07:08:42.298-07:00Trigonometry Graph - Transformation<h3>
GRAPH SKETCHING<br />ANALYSIS OF SINE GRAPHS</h3>
<i>in the following activities, post your responses as a comment.</i><br />
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<b>Activity 1:</b><br />
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Define the following terms, where possible identify the context when it is applied.<br />
A. Amplitude<br />
B. Wavelength<br />
C. Frequency<br />
D. Phase<br />
E. Characteristics of the Wave<br />
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<b>Activity 2:</b><br />
Study the following graphs with reference to y = sinx and (1) identify the transformation (s) of the graphs eg. enlargement, shift in x-direction. (2) State whether the new graph is similar to y = sinx. (3) suggest possible the 'transformed' equation. Note that x is in radian.<br />
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<b><span class="Apple-style-span" style="font-size: large;">original</span></b></div>
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y = sinx</div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjlMVYx4Ba_TM3EvTieJt5yc7-bsJiWof0-MOUWc9yLRwaGQOSo2s4WKGOBWRvvPMblOeF1cXDiR6HJXf1bPwh2T87yTo39lH8gLUXPsvKVM7hc4XhL_lR8ervBlvwEeJZEJx9JKfF3LTHv/s1600/Screen+shot+2013-07-25+at+AM+10.51.37.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="112" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjlMVYx4Ba_TM3EvTieJt5yc7-bsJiWof0-MOUWc9yLRwaGQOSo2s4WKGOBWRvvPMblOeF1cXDiR6HJXf1bPwh2T87yTo39lH8gLUXPsvKVM7hc4XhL_lR8ervBlvwEeJZEJx9JKfF3LTHv/s320/Screen+shot+2013-07-25+at+AM+10.51.37.png" width="320" /></a></div>
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<b><span class="Apple-style-span" style="font-size: large;">transformation 1</span></b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPj1ELtYZOrww24TJdOJfTg5VXaeUxokOXINDQLzWGtw8QsDjPtaARbpBe2SfVvwv5e3ZGj0T9d_7IbblxjnvAgqtk2bIIY6IuGrJcLuD5n0JvX64Aa7UL5hrKSUGTCmCtEfX8egtYXrai/s1600/Screen+shot+2013-07-25+at+AM+10.51.46.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="186" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPj1ELtYZOrww24TJdOJfTg5VXaeUxokOXINDQLzWGtw8QsDjPtaARbpBe2SfVvwv5e3ZGj0T9d_7IbblxjnvAgqtk2bIIY6IuGrJcLuD5n0JvX64Aa7UL5hrKSUGTCmCtEfX8egtYXrai/s320/Screen+shot+2013-07-25+at+AM+10.51.46.png" width="320" /></a></div>
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<b><span class="Apple-style-span" style="font-size: large;">transformation 2</span></b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglVYNutj4Boo5R8otkJsoNk8n3Rl4-hsXcSTPehuwb3Q9oNnqaRI402tP65kH4FyQh2fpeVq-73mhUCY7zGwO6o8LalSL5zymetMrkZ-Y07yCK-0S_ycggYhGIFZZYGHoHbOr9jre2qTx5/s1600/Screen+shot+2013-07-25+at+AM+10.51.51.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="106" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglVYNutj4Boo5R8otkJsoNk8n3Rl4-hsXcSTPehuwb3Q9oNnqaRI402tP65kH4FyQh2fpeVq-73mhUCY7zGwO6o8LalSL5zymetMrkZ-Y07yCK-0S_ycggYhGIFZZYGHoHbOr9jre2qTx5/s320/Screen+shot+2013-07-25+at+AM+10.51.51.png" width="320" /></a></div>
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<b><span class="Apple-style-span" style="font-size: large;">transformation 3</span></b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVInQYOu-f79y0ZdahC6H1ZmDwtFL2Qh9XrYOMeGVJ2L1B3jzNq54NwgDjSFL4ykTfFZlaA08pFFuJFgAXWRZ5AQ77EctdwhAKLkNYHsIaCYCmH2AjKtPsEPLE-VGhAoJucQHdVAZko_bG/s1600/Screen+shot+2013-07-25+at+AM+10.51.57.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="111" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVInQYOu-f79y0ZdahC6H1ZmDwtFL2Qh9XrYOMeGVJ2L1B3jzNq54NwgDjSFL4ykTfFZlaA08pFFuJFgAXWRZ5AQ77EctdwhAKLkNYHsIaCYCmH2AjKtPsEPLE-VGhAoJucQHdVAZko_bG/s320/Screen+shot+2013-07-25+at+AM+10.51.57.png" width="320" /></a></div>
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<b><span class="Apple-style-span" style="font-size: large;">transformation 4</span></b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiaJ47L5mlyfV0i_TamvuSl5t-gLYWSWbHHAuRxRmBBs4FChUAEXNPPnJOdUcCh3NimfE2L25AElHQpqYGDE8CoY8wV0TqWJT5zdPCmTaREy8TPOCE4aQAh0PnQJ1F_6RxEaK8_mhs3GvYp/s1600/Screen+shot+2013-07-25+at+AM+10.52.07.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="155" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiaJ47L5mlyfV0i_TamvuSl5t-gLYWSWbHHAuRxRmBBs4FChUAEXNPPnJOdUcCh3NimfE2L25AElHQpqYGDE8CoY8wV0TqWJT5zdPCmTaREy8TPOCE4aQAh0PnQJ1F_6RxEaK8_mhs3GvYp/s320/Screen+shot+2013-07-25+at+AM+10.52.07.png" width="320" /></a></div>
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<br />Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com1tag:blogger.com,1999:blog-7991892050140229718.post-65170973380101644182013-07-24T21:39:00.001-07:002013-07-24T21:40:44.286-07:00TI84 TRIG graphing<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGCmzC2D9zbt3YlnWslC9rgyb-AEGmUnc81DWYG2g8ujumqJPItUDEYwOOeLU8RIHyfXmidouev112mMU7lImLEaaWtjz5YyulhxtJYcJYqxaZruxxC13UlhWDlXKqQsZxKOmQiuW_sQk/s1600/Screen+shot+2013-07-25+at+PM+12.36.23.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="438" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGCmzC2D9zbt3YlnWslC9rgyb-AEGmUnc81DWYG2g8ujumqJPItUDEYwOOeLU8RIHyfXmidouev112mMU7lImLEaaWtjz5YyulhxtJYcJYqxaZruxxC13UlhWDlXKqQsZxKOmQiuW_sQk/s640/Screen+shot+2013-07-25+at+PM+12.36.23.png" width="640" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjzXpZWLGcycSD2brHqBImsV6yr5T9_uitkxoig5YU2sc436KLxDlCjBlY3L2mMcMC1xkUIqYMVDArw89TS3Qz1R0cm7EdVpdbjkJUR3OhtwJWbztYf-GRoElRl2xho4EeAYCXekjYoYs/s1600/Screen+shot+2013-07-25+at+PM+12.36.51.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="424" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjzXpZWLGcycSD2brHqBImsV6yr5T9_uitkxoig5YU2sc436KLxDlCjBlY3L2mMcMC1xkUIqYMVDArw89TS3Qz1R0cm7EdVpdbjkJUR3OhtwJWbztYf-GRoElRl2xho4EeAYCXekjYoYs/s640/Screen+shot+2013-07-25+at+PM+12.36.51.png" width="640" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgCXint_8jUuYg3Lfq6eRRtNOjzALfzoUktfYkfJnDi6JDKpb9XlqSsn26HEWbEro2PqWCTgIab9Ogi7HKQvFFpwZAJL41U61IKPxU7HGXOFVZlo1Yrzsh505dkE7qn9n15cHrb9chhPoU/s1600/Screen+shot+2013-07-25+at+PM+12.37.08.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="449" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgCXint_8jUuYg3Lfq6eRRtNOjzALfzoUktfYkfJnDi6JDKpb9XlqSsn26HEWbEro2PqWCTgIab9Ogi7HKQvFFpwZAJL41U61IKPxU7HGXOFVZlo1Yrzsh505dkE7qn9n15cHrb9chhPoU/s640/Screen+shot+2013-07-25+at+PM+12.37.08.png" width="640" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTUr_8TwH9_38msStsqNVDaljT9tLkSEaxAJSumQ_07PWo7wgAjBqI01ggUSi5F0ucLJMopJjSkdTvl0g-R3PZ3E59PIwMtpdnS-mrgXjgyXuO8TFichf1J2bd2rCYkkxv1bDwH4VfXdw/s1600/Screen+shot+2013-07-25+at+PM+12.37.21.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="462" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTUr_8TwH9_38msStsqNVDaljT9tLkSEaxAJSumQ_07PWo7wgAjBqI01ggUSi5F0ucLJMopJjSkdTvl0g-R3PZ3E59PIwMtpdnS-mrgXjgyXuO8TFichf1J2bd2rCYkkxv1bDwH4VfXdw/s640/Screen+shot+2013-07-25+at+PM+12.37.21.png" width="640" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9WOoZFe9bLuxtNW8lBxca1yIlGRM47krjqGglNDIjtiTwNXLN2pt-Trt85VoqrLTAVitbRpgQwHjIqh5jKjIdKRkzM5jvfZO9cnvI7e8Iw_4GC22DOVJH8hZi_bBCi5Ibsbzuu428Gi0/s1600/Screen+shot+2013-07-25+at+PM+12.37.33.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="219" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9WOoZFe9bLuxtNW8lBxca1yIlGRM47krjqGglNDIjtiTwNXLN2pt-Trt85VoqrLTAVitbRpgQwHjIqh5jKjIdKRkzM5jvfZO9cnvI7e8Iw_4GC22DOVJH8hZi_bBCi5Ibsbzuu428Gi0/s640/Screen+shot+2013-07-25+at+PM+12.37.33.png" width="640" /></a></div>
Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-7991892050140229718.post-17473797650960346022013-07-24T21:07:00.000-07:002013-07-24T21:07:22.884-07:00Summary of the lesson<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHiQot08zf8_r_528pCiZsWcgxlRRZIKn58Pecrjav3EducaNAgOLx7ZAtYpQWIgz_hSybcjsN9tOs1g9SCDUiTz4STN4VW4oGURcWpBModaNx9DHOEwa5NEuQOjrcuv4FpLsJd3GJMv2q/s1600/IMG_20130725_120002.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHiQot08zf8_r_528pCiZsWcgxlRRZIKn58Pecrjav3EducaNAgOLx7ZAtYpQWIgz_hSybcjsN9tOs1g9SCDUiTz4STN4VW4oGURcWpBModaNx9DHOEwa5NEuQOjrcuv4FpLsJd3GJMv2q/s320/IMG_20130725_120002.jpg" width="320" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSYan3eQaAaEalY1NeWS_GFhhhud2d0ViSF1mDo-BCzEC831HIT97nAdFbJK5mvDScs65oDk_VaqClyTVFS2jNxzEGJNLtC4k1Qpbc1UYmzTHXHfaz6oY4Mq2jfhyphenhyphen7shhensOMI1bB4GTW/s1600/PictureAmbitext.svg.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="154" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSYan3eQaAaEalY1NeWS_GFhhhud2d0ViSF1mDo-BCzEC831HIT97nAdFbJK5mvDScs65oDk_VaqClyTVFS2jNxzEGJNLtC4k1Qpbc1UYmzTHXHfaz6oY4Mq2jfhyphenhyphen7shhensOMI1bB4GTW/s320/PictureAmbitext.svg.png" width="320" /></a></div>
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Oh.<br />
Here are the conditions for the ambiguous case:<br />
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<ul style="background-color: white; font-family: sans-serif; font-size: 13px; line-height: 19.1875px; list-style-image: url(data:image/png; margin: 0.3em 0px 0px 1.6em; padding: 0px;">
<li style="margin-bottom: 0.1em;">The angle <i>A</i> is cute (i.e., A < 90°).</li>
<li style="margin-bottom: 0.1em;">The side <i>a</i> is shorter than the side <i>c</i> (i.e., <i>a</i> < <i>c</i>).</li>
<li style="margin-bottom: 0.1em;">The side <i>a</i> is longer than the altitude <i>h</i> from angle <i>B</i>, where <i>h</i> = <i>c</i> sin <i>A</i> (i.e., <i>a</i> > <i>h</i>).</li>
<li></li>
</ul>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7991892050140229718.post-58700741279356416292013-07-23T21:01:00.001-07:002013-07-24T17:30:18.096-07:00Unit circle - Sine Cosine and Tangent<div class="separator" style="clear: both; text-align: center;">
<a href="http://www.mathsisfun.com/algebra/trig-interactive-unit-circle.html" target="_blank"><img border="0" height="470" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEil13HfmSYtnXXfUp7D5vr23H9hzK1Lz1dYuPZUAXFU7iLMysv4GZfNIsuSOmnpBcmMPrNc9-DxJUSFkpnqUv2xr1dMgzTUz4RAHhCUgMt-zxJYvl2fKWpdWUu8xvfCSs76mW_wik7WiW0/s640/Screen+shot+2013-07-24+at+AM+11.51.12.png" width="640" /></a></div>
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<a href="http://www.mathsisfun.com/algebra/trig-interactive-unit-circle.html" target="_blank">link</a> to above diagram</div>
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<a href="http://curvebank.calstatela.edu/unit/unit.htm" target="_blank"><img border="0" height="276" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWOFLZPqhVcTexrGkTQrXy75e4_QJkrll7zOwXb9wIe0jtBVjUwjq9fzpYlSZskshMPTg6CvC0Qu13NzoKHF0YBVGfjZAKV5BY1-3H8rFignxcNyRVAAsHprwCZTl9heRr1leM8bQlUE4/s640/Screen+shot+2013-07-24+at+AM+11.54.34.png" width="640" /></a></div>
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<a href="http://curvebank.calstatela.edu/unit/unit.htm" target="_blank">link</a> to above diagram</div>
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<a href="http://www.math.utah.edu/~palais/cossin.html" target="_blank"><img border="0" height="430" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjfd6UdKU75gQwT1ecRFTRVOeAdSl_O1ND96JikVJCkVNlh18Bc2mXzxplv4CfFi1jOvSh4lkTGgZdnc0VAdiiDNR4Rr-8pekEV89YSer__70NuqI8_2d2fy3A9pD9BWs5yiO1oT0vwMSY/s640/Screen+shot+2013-07-24+at+AM+11.56.57.png" width="640" /></a></div>
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<a href="http://www.math.utah.edu/~palais/cossin.html" target="_blank">click</a> to above diagram</div>
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<a href="http://www.brokenairplane.com/2011/02/math-geogebra-trigonometry-circle.html" target="_blank"><img border="0" height="500" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2v8EdH3ZLS08qOWWURQSWPNfx5ov5xFr1_hrb2IzH9a9v1Qn4poWNOdr_pjPC0VNt-VSe-FKr1lt7HJ-Y6XQ1r8q7LgdYgn186KqLcyh_Li3LY8hv6oJJBFvv_q50f-svNwbeP4Z3oo0/s640/Screen+shot+2013-07-24+at+PM+12.01.44.png" width="640" /></a></div>
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<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://www.brokenairplane.com/2011/02/math-geogebra-trigonometry-circle.html" target="_blank">click </a>to above diagram</div>
<br />Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-7991892050140229718.post-24215322352567278652013-07-22T19:18:00.000-07:002013-07-22T19:19:24.260-07:00QUIZ B (SHORT ANSWER)QUIZ B: to be done on foolscap papers and submit<br />
<br />
QUESTION 1<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiH09ncYohz06WJopW0lUvKrAdMQwWOdaB0iAPwzWDTSZKseVAOiz1IOYFoC7ty6fCTX-4cESf7jUBLzoSRPtVRRmMl4byLJBBacOQkR_EQj8Cycqg_FByCsGwJAuWzXwJY7qDOk300ltw/s1600/Screen+shot+2013-07-23+at+AM+08.53.56.png" imageanchor="1"><img border="0" height="107" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiH09ncYohz06WJopW0lUvKrAdMQwWOdaB0iAPwzWDTSZKseVAOiz1IOYFoC7ty6fCTX-4cESf7jUBLzoSRPtVRRmMl4byLJBBacOQkR_EQj8Cycqg_FByCsGwJAuWzXwJY7qDOk300ltw/s640/Screen+shot+2013-07-23+at+AM+08.53.56.png" width="640" /></a><br />
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QUESTION 2<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidQpSmkE1vt6-T3HxYfmAjjtDgVBimPEs244i6PuI6OyGcsNaEnsI5S50IY3GKogdMl3zj4jbLdj5evY4rTanY1_fQwhkI244fOnbJSAtAn3oLgqnKIxpm4kUc6pZVkqX3z_obwez1QTY/s1600/Screen+shot+2013-07-23+at+AM+08.54.08.png" imageanchor="1"><img border="0" height="262" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidQpSmkE1vt6-T3HxYfmAjjtDgVBimPEs244i6PuI6OyGcsNaEnsI5S50IY3GKogdMl3zj4jbLdj5evY4rTanY1_fQwhkI244fOnbJSAtAn3oLgqnKIxpm4kUc6pZVkqX3z_obwez1QTY/s640/Screen+shot+2013-07-23+at+AM+08.54.08.png" width="640" /></a><br />
QUESTION 3<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwM9ZVTQcGjCszSLGjXeM4uOS_L0R_66pIfiWzLKk265ZcVkxx0WmQNHRSqp5leEcUzX0K-8-O8BiB84YH0QxTd5urGFBaG6uC0oqvq1QrchhkjBA6M75y3L-Ls34ybf7BSb3L9bh6AaQ/s1600/Screen+shot+2013-07-23+at+AM+08.54.21.png" imageanchor="1"><img border="0" height="246" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwM9ZVTQcGjCszSLGjXeM4uOS_L0R_66pIfiWzLKk265ZcVkxx0WmQNHRSqp5leEcUzX0K-8-O8BiB84YH0QxTd5urGFBaG6uC0oqvq1QrchhkjBA6M75y3L-Ls34ybf7BSb3L9bh6AaQ/s640/Screen+shot+2013-07-23+at+AM+08.54.21.png" width="640" /></a><br />
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QUESTION 4<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgy9OYpg57Sos0WSZL1oZBCTSE4myiviLe6bkmiVh6ZRbAJvng87KOOxy7c6JSDn4UY1TbM6qG9Thce_Re9_-uD22KmzP2PLP5JmLCYHDpK9Sd4_zr0dRaqMF9Mxoj6eLVXylX_wa-NRH0/s1600/Screen+shot+2013-07-23+at+AM+08.54.39.png" imageanchor="1"><img border="0" height="310" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgy9OYpg57Sos0WSZL1oZBCTSE4myiviLe6bkmiVh6ZRbAJvng87KOOxy7c6JSDn4UY1TbM6qG9Thce_Re9_-uD22KmzP2PLP5JmLCYHDpK9Sd4_zr0dRaqMF9Mxoj6eLVXylX_wa-NRH0/s640/Screen+shot+2013-07-23+at+AM+08.54.39.png" width="640" /></a>Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-7991892050140229718.post-1039428040022577292013-07-22T18:58:00.000-07:002013-07-22T18:58:33.066-07:00QUIZ A (MCQ)<iframe frameborder="0" height="500" marginheight="0" marginwidth="0" src="https://docs.google.com/forms/d/1-f7I3rPY_0icmzIe2jIQIga5UAdVioDDxOla1CjwkjU/viewform?embedded=true" width="760">Loading...</iframe>Nur Joharihttp://www.blogger.com/profile/12038483883275572574noreply@blogger.com0tag:blogger.com,1999:blog-7991892050140229718.post-40276203846710115522013-07-22T18:55:00.000-07:002013-07-22T18:55:18.400-07:00SUMMARY - TRIGONOMETRY EM<h3>
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SUMMARY OF TRIGONOMETRY </div>
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(ELEMENTARY MATHEMATICS)</div>
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