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Math Help - Fourier Series Integral Identities

  1. #1
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    Fourier Series Integral Identities

    For the Forier series whose Period is 2 and f(t) = cos( pie/2 * t)

    I have trouble getting the trig identity down.
    eventually I reach a_0 = 4 / pie
    but once I come to a_n
    I cannot understand how to integrate

    the integral of [ cos(nt) * cos(pie /2 * t) * dt] from -1 to 1

    I have tried integration by parts but to no avail


    Thank you for your time
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by stressedengineeringstuden View Post
    For the Forier series whose Period is 2 and f(t) = cos( pie/2 * t)

    I have trouble getting the trig identity down.
    eventually I reach a_0 = 4 / pie
    but once I come to a_n
    I cannot understand how to integrate

    the integral of [ cos(nt) * cos(pie /2 * t) * dt] from -1 to 1

    I have tried integration by parts but to no avail


    Thank you for your time
    Recall that \cos\alpha\cos\beta=\tfrac{1}{2}\left[\cos(\alpha+\beta)+\cos(\alpha-\beta)\right]. In your case, let \alpha=nt and \beta=\tfrac{1}{2}\pi t.

    Can you proceed?
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