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Fourier Series and deriving formulas for sums of numerical

  1. Feb 4, 2016 #1

    RJLiberator

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    Gold Member

    1. The problem statement, all variables and given/known data
    1.jpg 2.jpg

    2. Relevant equations


    3. The attempt at a solution

    So I am tasked with answer #3 and #4. I have supplied the indicated parenthesis of 8 also with the image.

    Here is my thinking:
    Take the fourier series for |sin(θ)|.
    Let θ = 0 and we see a perfect relationship.
    sin(0) = 0 and cos(0) = 1.
    So with just a little algebra and setting sin(θ) = the fourier series of sin(θ) We can easily show #3 part 1.
    Similiarly, with setting θ = pi/2 we can solve for #3 part b.

    Is this the correct way of going about this?
    I ask this question, even tho I have perfect results, as this seems too simple and I feel like I haven't used anything here. Is this really what the question is asking?
     
  2. jcsd
  3. Feb 4, 2016 #2

    blue_leaf77

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    Science Advisor
    Homework Helper

    Yes, that's correct.
     
  4. Feb 4, 2016 #3

    RJLiberator

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    Gold Member

    Oh, HELL yes.
    It feels so good to be able to solve one of my homework problems in less than 4 minutes for a change :D.
    MAN I feel great.

    Thank you.
     
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