# Fourier coefficients

errordude

## Homework Statement

Hi i would just like some fast hints, I'm doing the integrals wrong, I am splitting up the integral below and get the wrong answer.

well it's about finding the Fourier series for f(t)={0 for -π<t<0 and sint for 0≤t≤π}

## Homework Equations

$$a_{n} = \frac{1}{\pi}\int_{-\pi}^{\pi}f(t)\cos(nt) dt , n\in Z_{+}$$

## The Attempt at a Solution

well i split the integral up in finding $$a_{n}$$ like

$$\frac{1}{\pi}\int_{-\pi}^{\pi}f(t)\cos(nt) dt = \frac{1}{\pi}\int_{-\pi}^{0} 0· dt+\frac{1}{\pi}\int_{0}^{\pi}\sin(t)\cos(nt) dt$$
Both of these elementary, but it fails to produce the right series.
Hints anyone?

Homework Helper
Gold Member
Did you forget the bn?

errordude
Did you forget the bn?

no but that just get to zero

Homework Helper
Gold Member
no but that just get to zero

They can't be zero because the function you are expanding is not an even function.

errordude
They can't be zero because the function you are expanding is not an odd function.

That's what i was thinking

$$\frac{1}{\pi}\int_{-\pi}^{\pi}f(t)\sin(nt) dt = \frac{1}{\pi}\int_{-\pi}^{0} 0· dt+\frac{1}{\pi}\int_{0}^{\pi}\sin(t)\sin(nt) dt$$

but the above is zero!

i'm doing something wrong.

Homework Helper
Gold Member
I have to run now. You didn't show your work but I'm guessing you need to look what happens when n = 1.

errordude
halloo??

any1 who knows this Fourier series

f(t)={0 for -π<t<0 and sint for 0≤t≤π}

Homework Helper
Gold Member
Nobody is going to just give you the answer. Show us your work for the an and bn and we will help you find the mistake.

errordude
Nobody is going to just give you the answer. Show us your work for the an and bn and we will help you find the mistake.

Hey man chill.

b_1=1/2 that was the problem.

Homework Helper
Gold Member
Hey man chill.

b_1=1/2 that was the problem.

Chill?? Surely you mean "Thanks for the suggestion, eh?"

errordude
Chill?? Surely you mean "Thanks for the suggestion, eh?"

you were right LC, b_1 was the crucial step.

thanx