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Fourier Series

  1. Apr 15, 2009 #1
    1. The problem statement, all variables and given/known data
    { 0 -pi < t < 0
    E(t) =
    { sin(t) 0 < t < pi

    Find the fourier series
    w = 1, T = 2pi, L = pi
    a0 = 1/(2L) integral(-L to L) f(t) dt
    an = 1/(L) integral(-L to L) f(t)cos(nwt)dt n = 1,2,3...
    bn = 1/(L) integral(-L to L) f(t)sin(nwt)dt n = 1,2,3...

    3. The attempt at a solution
    now im able to find a0 but cannot find an. Im stuck at integrating

    an = (1/pi)*integral(0 to pi) sin(t)cos(nt) dt ***

    because of the "n" in the "cos" i cannot find the integral, first glance i though integration by parts but that just swaps the sin and cos's around. Than ive looked at the double angle rules and since "n" changes i figured i couldnt apply either since n = 1,2,3.... etc

    Any idea where to go in order to integrate it ?***
    bn is the same problem once i figure out how to integrate it, it should work out nicely

    Thanks in advance TRENT
     
  2. jcsd
  3. Apr 15, 2009 #2
    [tex]\sin x\cos y=\frac12\biggl(\sin(x+y)+\sin(x-y)\biggr)[/tex]
     
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