Finding the Fourier Series of E(t)

[Trenthan]

Homework Statement

{ 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
a_n = 1/(L) integral(-L to L) f(t)cos(nwt)dt n = 1,2,3...
b_n = 1/(L) integral(-L to L) f(t)sin(nwt)dt n = 1,2,3...

The Attempt at a Solution

now I am able to find a₀ but cannot find a_n. I am stuck at integrating

a_n = (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 I've looked at the double angle rules and since "n" changes i figured i couldn't apply either since n = 1,2,3... etc

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

Thanks in advance TRENT

 

[Billy Bob]

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