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Orthogonality of Sine and Cosine functions

  1. Jun 10, 2009 #1
    Hi,

    would anyone be able to explain how to evaluate a function using orthogonality (i.e. using orthogonality to solve a definite integration problem with sines/cosines)?

    Thank you
     
  2. jcsd
  3. Jun 10, 2009 #2
  4. Jun 11, 2009 #3
    Orthogonality in a vector space means that the inner product of two vectors is 0. In this case, your space is a function space so the inner product is defined as the integral of the product of the functions.

    http://en.wikipedia.org/wiki/Orthogonal#Orthogonal_functions
     
  5. Jun 12, 2009 #4
    I would look in (already referenced in post #2 By ExactlySolved)
    http://mathworld.wolfram.com/FourierSeries.html
    And in particular look at Eqns (8) and (9) for solving for the coefficients in a Fourier series. Also look at (18) and (19). The sine-like and cosine-like terms are orthogonal, as proved by integrating their product over the interval 0 to 2 pi.
     
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