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166 lines
9.3 KiB
HTML
166 lines
9.3 KiB
HTML
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<title>Sine Function - Graph Exercise</title>
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<div id="content" role="main"><!-- #BeginEditable "Body" -->
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<h1 align="center">Sine Function - Graph Exercise</h1>
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<p align="center"><img src="images/sine.gif" width="360" height="173" border="1" alt="sine wave" /><br />
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<span class="Larger">The Sine Function produces a very beautiful curve,<br />
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but don't take our word for it, make your own!</span></p>
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<h2>Sine Function</h2>
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<p>First, read the page on <a href="sine-cosine-tangent.html">Sine, Cosine and Tangent</a>.</p>
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<p>Now you will know that the sine of any angle is the length of the far side of the triangle (the "opposite")
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divided by the long side (the "hypotenuse"):</p>
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<p align="center"><img src="algebra/images/adjacent-opposite-hypotenuse.svg" alt="adjacent opposite hypotenuse" /><br />
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<span class="Larger">Sine of <b>θ</b> = Opposite / Hypotenuse</span></p>
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<h2>Draw Triangles</h2>
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<p>To make the graph, we need to calculate the sine for different angles, then put those points on a graph, and
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then "join the dots".</p>
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<h3>Step 1: Draw the Angled Lines</h3>
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<p>Place a mark at the center of a piece of paper, then, using a <a href="geometry/protractor-using.html">protractor</a>, mark every 15 degrees from 0°
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to 180° in a semi-circle. Then rotate the protractor and mark from 180° around to the start again. Then
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draw lines radiating from the center to each of your marks so that you end up with an illustration like this:</p>
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<div align="center"><a href="images/radiating-15-large.gif"><img src="images/radiating-15-small.gif" width="162" height="166" border="0" alt="radiating 15 small" /></a>
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<br />
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Lines at 15° (click to enlarge)</div>
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<p>Or, you can click on the above illustration, then print out the result.</p>
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<h3>Step 2: Draw and Measure the Triangles</h3>
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<p>We can now turn each of those lines into a triangle, example:</p>
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<p align="center"><img src="images/radiating-triangle-1.gif" width="182" height="131" border="0" alt="radiating triangle 1" /></p>
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<h2>Measure Triangles</h2>
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<p>When you have completed each triangle, it is simply a matter of measuring the lines. Remember that the sine
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is <i>the length of the line opposite the angle</i> <b>divided by</b> <i>the hypotenuse</i> (which should all
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be the same length if you have drawn it well) </p>
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<p align="center"><img src="algebra/images/sine-graph-triangle.svg" alt="radiating triangle 2" /></p>
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<p>Write all your measurements in a table. This is what I got, but your measurements may be different:</p>
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<table width="433" border="0" align="center">
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<tr bgcolor="#FF99FF">
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<td width="59">
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<div align="center"><b>Angle</b></div> </td>
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<td width="102">
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<div align="center"><b>Opposite</b></div> </td>
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<td width="96">
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<div align="center"><b>Hypotenuse</b></div> </td>
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<td width="158">
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<div align="center"><b>Opposite / Hypotenuse</b></div> </td>
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</tr>
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<tr bgcolor="#FFCCFF">
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<td width="59">
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<div align="center">0°</div> </td>
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<td width="102">
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<div align="center">0 mm</div> </td>
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<td width="96">
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<div align="center">86 mm</div> </td>
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<td width="158">
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<div align="center">0.00</div> </td>
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</tr>
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<tr bgcolor="#FFCCFF">
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<td width="59">
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<div align="center">15°</div> </td>
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<td width="102">
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<div align="center">22 mm</div> </td>
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<td width="96">
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<div align="center">86 mm</div> </td>
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<td width="158">
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<div align="center">0.26</div> </td>
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</tr>
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<tr bgcolor="#FFCCFF">
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<td width="59">
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<div align="center">30°</div> </td>
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<td width="102">
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<div align="center">43 mm</div> </td>
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<td width="96">
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<div align="center">86 mm</div> </td>
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<td width="158">
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<div align="center">0.50</div> </td>
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</tr>
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<tr>
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<td colspan="4">
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<div align="center">etc ...</div> </td>
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</tr>
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</table>
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<p>You can print a table ready to fill in <a href="sine-graph-table.html">here</a>.</p>
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<p><b>Important: When the "opposite" line goes downwards it is negative.</b></p>
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<p><i>Tip: if you have drawn it well, you can take advantage of the symmetry of 0-90, 90-180, 180-270 and 270-360.</i></p>
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<h2>Graph The Results</h2>
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<p>Get some graph paper and prepare it by scaling off 0 to 360 in 15 increments along the x-axis, and scaling
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off -1 to +1 on the y-axis. You can use your own graph paper, or print out <a href="graph-5x6.html">this graph
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paper</a></p>
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<p>Now plot each point from the table on the graph.</p>
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<p>Then join the dots as neatly as you can.</p>
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<h2>Result</h2>
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<p>The result should look something like the graph at the very top. </p>
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<p>But you have done much more than draw a nice curve. You have :</p>
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<ul>
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<li>learned about one of the most important functions in mathematics</li>
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<li>learned that you don't have to believe what people say - you can try it for yourself.</li>
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<li>had experience plotting graphs</li>
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<li>learned how symmetry can save effort</li>
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</ul>
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<p>Hope you enjoyed !</p>
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<div class="related">
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<a href="sine-cosine-tangent.html">Sine, Cosine and Tangent</a>
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<a href="algebra/trigonometry.html">Trigonometry Index</a> </div>
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Copyright © 2017 MathsIsFun.com
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