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Fourier series

  1. Jul 1, 2007 #1
    expand the function y=sinx in a series of cosines in the interval (0 to 180)
    i want to know only the value of f(x) for solving this.what is the value of
    f(x).
     
  2. jcsd
  3. Jul 1, 2007 #2
    expand the function y=sinx in a series of cosines in the interval (0 to 180)
    i want to know only the value of f(x) for solving this.what is the value of
    f(x).
     
  4. Jul 1, 2007 #3

    chroot

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    Gold Member

    I suggest you post the entire problem, exactly as it was given to you. Next, show us your attempts at a solution, and where you've gotten stuck.

    - Warren
     
  5. Jul 2, 2007 #4
    to solve this problem first we need to know the value of An and A0
    ie the series is A0/2+SUMATION n=1 to infinity (An cosnx)where An is given by An=2/pie integral of -pie to +pie f(x)cosnx dx
    now what is the value of f(x) to substitute in that place to solve it.pls tell me.
     
  6. Jul 2, 2007 #5
    To solve this problem first we need to know the value of An and A0
    ie the series is A0/2+SUMATION n=1 to infinity (An cosnx)where An is given by An=2/pie integral of -pie to +pie f(x)cosnx dx
    now what is the value of f(x) to substitute in that place to solve it.pls tell me.
     
  7. Jul 2, 2007 #6

    CompuChip

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    [tex]f(x) = \sin(x)[/tex]?
    Why do you have two names (y and f(x) for the same thing?)
    At least, that's what you said in your first (two) post(s).
     
    Last edited: Jul 2, 2007
  8. Aug 13, 2007 #7
    cos(nx) is an even function. So you have to even extend the function[tex]f(x) = \sin(x)[/tex] first.
    It will be a periodic function of period [tex]2L = \pi[/tex].
    Then the coefficient
    [tex]a_n = \frac{2}{\pi/2} \int{\sin(x)\cos(2nx) dx}[/tex]
    integrate from 0 to [tex]\frac{\pi}{2} [/tex]
    which simplify to
    [tex]a_n = -\frac{2}{\pi (4n^2-1)} [/tex]

    The Fourier series is then
    [tex]\sin(x) = \frac{2}{\pi} -\frac{4}{\pi}(\frac{\cos(2x)}{1.3} + \frac{\cos(4x)}{3.5} + . . . ) [/tex]
     
    Last edited: Aug 13, 2007
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