https://calculus.subwiki.org/w/index.php?title=Cosine_function&feed=atom&action=history Cosine function - Revision history 2020-08-11T21:39:49Z Revision history for this page on the wiki MediaWiki 1.29.2 https://calculus.subwiki.org/w/index.php?title=Cosine_function&diff=269&oldid=prev Vipul: Created page with "{{particular function}} {{angular function radian convention}} ==Definition== ===Unit circle definition=== The '''cosine function''', denoted $\cos$, is defined as f..." 2011-09-05T20:59:56Z <p>Created page with &quot;{{particular function}} {{angular function radian convention}} ==Definition== ===Unit circle definition=== The &#039;&#039;&#039;cosine function&#039;&#039;&#039;, denoted &lt;math&gt;\cos&lt;/math&gt;, is defined as f...&quot;</p> <p><b>New page</b></p><div>{{particular function}}<br /> {{angular function radian convention}}<br /> ==Definition==<br /> <br /> ===Unit circle definition===<br /> <br /> The '''cosine function''', denoted &lt;math&gt;\cos&lt;/math&gt;, is defined as follows.<br /> <br /> Consider the unit circle centered at the origin, described as the following subset of the coordinate:<br /> <br /> &lt;math&gt;\{ (x,y) \mid x^2 + y^2 = 1\}&lt;/math&gt;<br /> <br /> For a real number &lt;math&gt;t&lt;/math&gt;, we define &lt;math&gt;\cos t&lt;/math&gt; as follows:<br /> <br /> * Start at the point &lt;math&gt;(1,0)&lt;/math&gt;, which lies on the unit circle centered at the origin.<br /> * Move a distance of &lt;math&gt;t&lt;/math&gt; along the unit circle in the counter-clockwise direction (i.e., the motion begins in the first quadrant, with both coordinates positive).<br /> * At the end, the &lt;math&gt;x&lt;/math&gt;-coordinate of the point thus obtained is defined as &lt;math&gt;\cos t&lt;/math&gt;.<br /> <br /> ===Triangle ratio definition (works for acute angles)===<br /> <br /> For an acute angle &lt;math&gt;t&lt;/math&gt;, i.e., for &lt;math&gt;t&lt;/math&gt; in the [[open interval]] &lt;math&gt;(0,\pi/2)&lt;/math&gt;, &lt;math&gt;\cos t&lt;/math&gt; can be defined as follows:<br /> <br /> * Construct any right triangle with one of the acute angles equal to &lt;math&gt;t&lt;/math&gt;.<br /> * &lt;math&gt;\! \cos t&lt;/math&gt; is the ratio of the leg adjacent to the angle &lt;math&gt;t&lt;/math&gt; to the hypotenuse.</div> Vipul