# Fourier Series

1. Apr 15, 2009

### Trenthan

1. The problem statement, all variables and given/known data
{ 0 -pi < t < 0
E(t) =
{ sin(t) 0 < t < pi

Find the fourier series
w = 1, T = 2pi, L = pi
a0 = 1/(2L) integral(-L to L) f(t) dt
an = 1/(L) integral(-L to L) f(t)cos(nwt)dt n = 1,2,3...
bn = 1/(L) integral(-L to L) f(t)sin(nwt)dt n = 1,2,3...

3. The attempt at a solution
now im able to find a0 but cannot find an. Im stuck at integrating

an = (1/pi)*integral(0 to pi) sin(t)cos(nt) dt ***

because of the "n" in the "cos" i cannot find the integral, first glance i though integration by parts but that just swaps the sin and cos's around. Than ive looked at the double angle rules and since "n" changes i figured i couldnt apply either since n = 1,2,3.... etc

Any idea where to go in order to integrate it ?***
bn is the same problem once i figure out how to integrate it, it should work out nicely

$$\sin x\cos y=\frac12\biggl(\sin(x+y)+\sin(x-y)\biggr)$$