When do the sine components of a Fourier series vanish?

Question

A Fourier series is given by:

$$ s_N(x) = \sum c_n \cdot e^{i \frac{2\pi n x}{P}} $$

With Euler's identity, the exponential can be converted to a sums of sines and cosines.

When do the sine components of a Fourier series vanish?

Answer 1

When you are dealing with an even function. -- Jack D'Aurizio

When $c_n=c_{-n}$ for all $n$. -- Henning Makholm