Cosine

Geometrically, the cosine is a projection of the complex number exp(−ix) to the real axis. The behavior of the cosine function can be studied in the following interactive figure, where you can drag the point x and observe the behaviour of the complex number exp(−ix) and the value of cosine(x).

 
0,0
–o+←↓↑→
x
cos
 

  
0,0
–o+←↓↑→
A
exp(ix)
cos