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Definition of the cosine

The cosine is per definition the first coordinate on the unit circle.

 


Explanation

Take a point P (x, y) on the unit circle. Then, per definition, the cosine of θ is the first coordinate of P and the sine is the second coordinate.

In this way obtuse angles can also have a sine or cosine. The name cosine comes from complementary sine. There are only two functions f (x) and (x) complying with the conditions

and these are the sine and the cosine, as

 


Example 1

You can see in the picture that cos (0) = cos (2π) = 1 and cos (90°) = cos (½π) = 0 and cos (180°) = cos (π) = −1.

 


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