TITLE: Why sin and cos in the Fourier Series?
QUESTION [13 upvotes]: Is there any special reason that we use the sines and cosines functions in the Fourier Series, while we know that if we chose any maximal orthonormal system in L2, we would get the same result? 
Is it something historical or what?
Thanks in advance.

REPLY [2 votes]: Nobody mentioned that $e^{2\pi inz}$ are the characters of $S^1$.