# Changes

## Cosine function

, 20:59, 5 September 2011
Created page with "{{particular function}} {{angular function radian convention}} ==Definition== ===Unit circle definition=== The '''cosine function''', denoted $\cos$, is defined as f..."
{{particular function}}
==Definition==

===Unit circle definition===

The '''cosine function''', denoted $\cos$, is defined as follows.

Consider the unit circle centered at the origin, described as the following subset of the coordinate:

$\{ (x,y) \mid x^2 + y^2 = 1\}$

For a real number $t$, we define $\cos t$ as follows:

* Start at the point $(1,0)$, which lies on the unit circle centered at the origin.
* Move a distance of $t$ along the unit circle in the counter-clockwise direction (i.e., the motion begins in the first quadrant, with both coordinates positive).
* At the end, the $x$-coordinate of the point thus obtained is defined as $\cos t$.

===Triangle ratio definition (works for acute angles)===

For an acute angle $t$, i.e., for $t$ in the [[open interval]] $(0,\pi/2)$, $\cos t$ can be defined as follows:

* Construct any right triangle with one of the acute angles equal to $t$.
* $\! \cos t$ is the ratio of the leg adjacent to the angle $t$ to the hypotenuse.
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