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156 lines
6.9 KiB
HTML
156 lines
6.9 KiB
HTML
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<title>Graphs of Sine, Cosine and Tangent</title>
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<meta name="description" content="The Sine Function has this beautiful up-down curve which repeats every 360 degrees:">
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Graphs of Sine, Cosine and Tangent</h1>
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<p class="center"><i>A sine wave made by a circle:</i></p>
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<div class="script" style="height: 230px;">
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images/circle-sine.js
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</div>
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<p class="center"><i>A sine wave produced naturally by a bouncing spring:</i></p>
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<iframe src="../physics/ispring.html" scrolling="no" style="width:362px; height:392px; overflow:hidden; margin:auto; display:block; border: none; background-color:#def;"></iframe>
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<h2>Plot of Sine</h2>
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<p style="float:right; margin: 0 0 5px 10px;"> </p>
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<span style="float:right; margin: 0 0 5px 10px;"><img src="images/sine-graph.svg" alt="sine graph" height="184" width="405"></span>
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<p>The Sine Function has this beautiful up-down curve (which repeats every 2<span class="times">π</span> radians, or 360°).</p>
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<p>It starts at <b>0</b>, heads up to <b>1</b> by <span class="times">π</span>/2 radians (90°) and then heads down to <b>−1</b>.</p>
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<div style="clear:both"></div>
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<h2>Plot of Cosine</h2>
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<p style="float:right; margin: 0 0 5px 10px;"> </p>
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<span style="float:right; margin: 0 0 5px 10px;"><img src="images/cosine-graph.svg" alt="cosine graph" height="184" width="413"></span>
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<p>Cosine is just like Sine, but it starts at 1 and heads down until <span class="times">π</span> radians (180°) and then heads up again.</p>
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<div style="clear:both"></div>
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<h2>Plot of Sine and Cosine</h2>
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<p style="float:right; margin: 0 0 5px 10px;"> </p>
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<span style="float:right; margin: 0 0 5px 10px;"><img src="images/sine-cosine-graph.svg" alt="sine cosine graph" height="184" width="405"></span>
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<p>In fact Sine and Cosine are like <b>good friends</b>: they follow each other, exactly <span class="times">π</span>/2 radians (90°) apart.</p>
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<div style="clear:both"></div>
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<h2>Plot of the Tangent Function</h2>
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<p style="float:right; margin: 0 0 5px 10px;"> </p>
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<span style="float:right; margin: 0 0 5px 10px;"><img src="images/tangent-graph.svg" alt="tangent graph" height="214" width="396"></span>
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<p>The Tangent function has a completely different shape ... it goes between negative and positive <a href="../numbers/infinity.html">Infinity</a>, crossing through 0, and at every <span class="times">π</span> radians (180°), as shown on this plot.</p>
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<p>At <span class="times">π</span>/2 radians (90°), and at −<span class="times">π</span>/2 (−90°), 3<span class="times">π</span>/2 (270°), etc, the function is officially <b>undefined</b>, because it could be <b>positive Infinity</b> or<b> negative Infinity</b>.</p>
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<div style="clear:both"></div>
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<h2>Inverse Sine, Cosine and Tangent</h2>
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<p>The <a href="trig-inverse-sin-cos-tan.html">Inverse Sine, Cosine and Tangent</a> graphs are:</p>
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<table style="border: 0;">
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<tbody>
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<tr>
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<td> </td>
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</tr>
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</tbody></table>
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<p class="center" style="float:left; margin: 0 10px 5px 0;"><span class="center" style="float:left; margin: 0 10px 5px 0;"><img src="images/inverse-sine-graph.svg" alt="inverse sine graph" height="220" width="183"></span><br>
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<span class="larger">Inverse Sine</span></p>
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<p class="center" style="float:right; margin: 0 0 5px 10px;"><span class="center" style="float:right; margin: 0 0 5px 10px;"><img src="images/inverse-cosine-graph.svg" alt="inverse cosine graph" height="234" width="176"></span><br>
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<span class="larger">Inverse Cosine</span></p>
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<div style="clear:both"></div>
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<p class="center"><img src="images/inverse-tangent-graph.svg" alt="inverse tangent graph" height="145" width="301"><br>
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<span class="larger">Inverse Tangent</span></p>
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<p class="center"><br></p>
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<div class="center80">
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<h3>Mirror Images</h3>
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<p>Here is <b>Cosine</b> and <b>Inverse Cosine</b> plotted on the same graph:</p>
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<p class="center"><img src="images/cosine-mirror-graph.svg" alt="cosine mirror graph" height="250" width="250"><br>
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<span class="larger">Cosine and Inverse Cosine </span></p>
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<p>They are mirror images (about the diagonal)!</p>
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<p>The same is true for <b>Sine</b> and <b>Inverse Sine</b> and for <b>Tangent</b> and <b>Inverse Tangent</b>. Can you see this in the graphs above?</p>
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</div>
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<p> </p>
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<div class="related">
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<a href="trigonometry-index.html">Trigonometry Index</a>
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<a href="../sine-cosine-tangent.html">Sine, Cosine and Tangent</a>
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<a href="small-angle-approximations.html">Small Angle Approximations</a>
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<a href="../geometry/unit-circle.html">Unit Circle</a>
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</div>
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<div id="copyrt">Copyright © 2022 Rod Pierce</div>
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