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Unit circle

The unit circle is the circle of radius 1 centered at the origin (0, 0).

 


Explanation

The cosine of θ is by definition the first coordinate of the point P (x, y) on the unit circle 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

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

 


Example 2

In the picture you can see that sin (0) = sin (π) = sin (2π) = 0 and sin (90°) = sin (½π) = 1.

 


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