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Problem with the fourier series

  1. Jun 12, 2012 #1
    1. The problem statement, all variables and given/known data

    this comes from a problem with the fourier series

    Screenshot2012-06-12at52252AMcopy.png


    3. The attempt at a solution

    I don't get the above step.
     
  2. jcsd
  3. Jun 12, 2012 #2
    What is cos(0)? How about cos(π)? cos(2π)? What's the period of cosine?
     
  4. Jun 12, 2012 #3
    here's another photo. I think the period is pi, but I would think cos npi would simplify to 1 not -1
     
  5. Jun 12, 2012 #4

    HallsofIvy

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    Staff Emeritus
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    I have no idea why you would think that! Surely you know that [itex]cos(\pi)= -1[/itex]?
     
  6. Jun 12, 2012 #5
    The period of cos is not ∏. Think at what intervals does cos give you the same numbers it was giving for the previous interval?

    In other words,

    [tex]cos(T+x) = cos(x)[/tex]

    For which smallest non-zero, positive value of T??


    Also, cos(n∏) has both the possibilities of being cos(∏) at n=1 and cos(2∏) at n=2. What are the values of each?
     
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