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The sine is by definition the second coordinate on the unit circle.



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

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

and these are the sine and the cosine, as


Example 1

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



The abbreviation sin was first used by the French mathematician Albert Girard (1595 - 1632).

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