Solving Fourier Coefficients: Hints for Finding a_n

[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?

 

[LCKurtz]

Did you forget the b_n?

 

[errordude]

Did you forget the b_n?

no but that just get to zero

 

[LCKurtz]

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.

 

[LCKurtz]

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}

 

[LCKurtz]

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

 

[errordude]

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

Hey man chill.

b_1=1/2 that was the problem.

 

[LCKurtz]

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