# 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.

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