Homework Help: Fourier series help

1. Feb 2, 2012

Kuma

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

Hi. I want to find the fourier series of

sin^2 x + sin ^3x

and sin θ = [e^iθ - e-iθ]/2i

2. Relevant equations

3. The attempt at a solution

So if i use sin x = [e^ix - e-ix]/2i I will get for the first term:

[e^2ix + e^-2ix -2]/-4

I can do the same for the second term but what do i do from here..? I'm not sure how to integrate these.

2. Feb 2, 2012

sunjin09

Your Fourier coefficients for sin2x are simply ±1/(2i) for exp(±2ix), similar for all the other terms

3. Feb 2, 2012

vela

Staff Emeritus
You don't need to integrate.

Hint: Use $\cos \theta = \frac{e^{i\theta}+e^{-i\theta}}{2}$ to rewrite

$$-\frac{e^{i(2x)} + e^{-i(2x)} - 2}{4} = \ ?$$

4. Feb 2, 2012

Kuma

isn't that just cos^2x ?? It should most likely be something else but that's the only way i see it being re written as cos. That just brings me back to the starting point so yeah..heh

5. Feb 2, 2012

vela

Staff Emeritus
No, you have to get the algebra right. You should know from trig that
$$\sin^2 x = \frac{1-\cos 2x}{2}$$ Can you see how to get that result from
$$\sin^2 x = -\frac{e^{i(2x)} + e^{-i(2x)} - 2}{4}$$using the hint I mentioned above.