In trig FS, you evaluate each component a0, an, bn. Well the exponential replaces that I think.
im guessing you use Euler's Rules (i think) to evaluate it which says
sin theta = 1 / 2i [ e ^ i*theta - e ^ -i*theta]
cos theta = 1 /2 [ e ^ i*theta + e ^ -i*theta]
Hopefully that answered...