# Homework Help: Cn coefficient for a Fourier series

1. Mar 1, 2012

### sekowe

1. The problem statement, all variables and given/known data

I have an example were they determine the Cn coefficient for a Fourier series:

My problem is i don't follow what happens in the following moment:

neither am i sure how the two e^-inwt comes to be cos(nwt) in the last part.

2. Relevant equations

3. The attempt at a solution

The only solution I can come up with is to reverse the limits what is obvious and then say: t=-a --> -1*t=-1*-a and then change a for -a in the limit and t for -t. However this doesn't work in other similar problems so I don't think think this is right.

2. Mar 1, 2012

### tiny-tim

welcome to pf!

hi sekowe! welcome to pf!

there's a misprint

the first exponent in the third line should be positive

between the second and third lines, they've substituted u = -t, du = -dt, and then renamed u as t again!

and of course the corrected third line lets you use eix + e-ix = (cosx)/2

3. Mar 1, 2012

### sekowe

A misprint... Yeah that clears up a lot :D

Thank you very much!