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Fourier series, please help

  1. Jun 8, 2008 #1
    fourier series, please help!!!

    1. The problem statement, all variables and given/known data
    Find the fourier series of f(x)=(sin x)^2.

    2. Relevant equations

    3. The attempt at a solution

    I know that I need to use the double angle formulas for this problem:
    (sin x)^2=1/2-1/2(cos 2x)
    but I do not know where to go from here.
  2. jcsd
  3. Jun 8, 2008 #2


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    All you have to do is calculate the coefficients of the Fourier series... which boils down to computing an integral. See your notes.
  4. Jun 8, 2008 #3
    I was told that no integration was needed for this problem and it basically boils down to trig identities.
  5. Jun 8, 2008 #4
    Do you know what the Fourier Series is for cos(x)? I'd imagine you could just do you substitution and then use Fourier tables and the like to make that entire thing a Fourier series.
  6. Jun 8, 2008 #5


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    When you used the trig identity you have already written down the cosine series. It has a cos(0*x) term and a cos(2*x) term. What are the coefficients? That IS a fourier series. Do you want it in some other form?
  7. Jun 9, 2008 #6


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    Definitely no integration is needed for this problem. Do you understand what a Fourier series is? It is a sum of functions of the form cos(nx) and sin(nx)! What is the Taylor's series, about x= 1 for (x-1)2? What is the Fourier seiries for cos(x)? What is the Fourier series for sin(2x)?
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