Sine

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The sine is a projection of the complex number exp(−ix) (which is a point on the unit circle in the complex plane) to the imaginary axis on the complex plane. In the following interactive figure, you can drag the point x on the real axis and observe the behaviour of the complex number exp(−ix) and the varying value of sine(x).

Sine Unit Circle on the Complex Plane

read more about sine on Bookofproofs