Cosine

The cosine is a projection of the complex number exp(−ix) (which is a point on the unit circle in the complex plane) to the real 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 cosine(x).

Cosine	Unit Circle on the Complex Plane
0,0 –o+←↓↑→ x cos	0,0 –o+←↓↑→ A exp(ix) cos

read more about cosine on Bookofproofs