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

Created page with "{{particular function}} {{angular function radian convention}} ==Definition== ===Unit circle definition=== The '''cosine function''', denoted <math>\cos</math>, is defined as f..."

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{{particular function}}
{{angular function radian convention}}
==Definition==

===Unit circle definition===

The '''cosine function''', denoted <math>\cos</math>, is defined as follows.

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

<math>\{ (x,y) \mid x^2 + y^2 = 1\}</math>

For a real number <math>t</math>, we define <math>\cos t</math> as follows:

* Start at the point <math>(1,0)</math>, which lies on the unit circle centered at the origin.
* Move a distance of <math>t</math> 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 <math>x</math>-coordinate of the point thus obtained is defined as <math>\cos t</math>.

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

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

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

Cosine function - Revision history

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

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