# Fourier Series of Cos(x)

1. Dec 6, 2008

### Osmano

Hello, I'm having some trouble completing a Fourier series question.

We have f(x)=Cos(x), for abs(x)≤π/2
f(x)=0, for π/2≤abs(x)≤π
period=2π

and then show that the Fourier series f(x) reads

now I can get the 1/π and the sum, as an=

and working through from there, the only part I'm having trouble with is the origin of the half cos(x) term. As far as I'm able to apply the fourier series I don't see where it comes from. (Bn must equal 0 right?)

2. Dec 6, 2008

### neo86

How did you deduce, that the Bn are zero? The orthogonality relation between sin and cos only holds if you integrate from 0 to 2pi, but in this case you integrate only from 0 to pi/2.