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Math Help - Fourier series for sin(2x) + cos(5x)

  1. #1
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    Exclamation Fourier series for sin(2x) + cos(5x)

    I am having trouble finding the real and complex Fourier series for the following:

    sin(2x) + cos(5x)

    If someone could do the first few steps, I'm sure I could manage the rest.

    So for an = 1/2pi x integral of (sin(2x)cos(kx) + cos(5x)cos(kx)) between 0, 2pi.... I'm not sure how to manipulate the equation

    Am I supposed to use the following: cos(A)cos(B) = (1/2)(cos(A+B) - cos(A-B))?

    Kindest regards <3
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  2. #2
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    Re: Fourier series for sin(2x) + cos(5x)

    Hey katspaws.

    Use your hint plus the fact sin(kx)cos(mx) is 0 because they are orthogonal if m and k integers.
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