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Homework Help: Fourier series help

  1. Feb 2, 2012 #1
    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. jcsd
  3. Feb 2, 2012 #2
    Your Fourier coefficients for sin2x are simply ±1/(2i) for exp(±2ix), similar for all the other terms
     
  4. Feb 2, 2012 #3

    vela

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    You don't need to integrate.

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

    $$-\frac{e^{i(2x)} + e^{-i(2x)} - 2}{4} = \ ?$$
     
  5. Feb 2, 2012 #4
    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
     
  6. Feb 2, 2012 #5

    vela

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    No, you have to get the algebra right. :wink: 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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