# Fourier series

1. Feb 19, 2009

### briteliner

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

find the fourier series for the function

0 -pi<x<pi
f(x)={
sinx 0<x<pi

2. Relevant equations

3. The attempt at a solution
I don't know how to do this and can't find a good explanation anywhere, any kind of help is appreciated...even just a push in the right direction

Last edited: Feb 19, 2009
2. Feb 19, 2009

### Dr.D

Are you saying your function is
f(x) = 0 x<-pi
= sin(x) 0<x<pi
= 0 x>pi
If so, that is not periodic and does not have a Fourier series in the usual sense, although it probably has a Fourier transform. Is that what you want?

3. Feb 19, 2009

### briteliner

we are supposed to assume that the function is continued outside of the interval with period 2pi periodically.
i just realized there was a mistake with the bounds also, but i fixed it now. it is a piecewise function which equals 0 from -pi to pi and sinx from 0 to pi

4. Feb 19, 2009

### Dick

I'm going to guess that the problem is to find the fourier series on the interval [-pi,pi] of the function f(x)=sin(x) for x in [0,pi] and f(x)=0 for x in [-pi,0]. If so, then the coefficients of that series are defined in terms of integrals of sin(x) times sin(nx) and cos(nx). Since f(x)=0 for x<0, just integrate from 0 to pi. Can you do any of them?

5. Feb 19, 2009

### briteliner

ok thanks so then i have integral from 0 to pi of sinxcosnx dx. would this just give 0 since sinx is odd and cosnx is even, giving an odd function?

6. Feb 19, 2009

### Dick

7. Feb 19, 2009

### briteliner

oh right. thanks so much!