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Orthogonality of sine and cosine question

  1. Jun 10, 2014 #1
    Hello,

    I'm trying to solve Fourier Series, but I have a question.
    I know that cos(nx) is even and sin(nx) is odd. But what does this mean when I take the integral or sum of cos(nx) or sin(nx)? Do they have a value or do they just keep their form?
     
  2. jcsd
  3. Jun 10, 2014 #2

    Simon Bridge

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    $$\int_a^a \sin kx \; dx = 0\\
    \int_a^a \cos kx \; dx = 2\int_0^a \cos kx\; dx$$
    ... with the fourier series you are more interested in the integral of f(x) multiplied by a sine or a cosine though.
     
  4. Jun 11, 2014 #3
    I found the answer to my own question.
    I wasn't concerned about cos(nx), but by cos(npi) which is equal to (-1)^n and for sin(npi) it's equal to 0. I now understand that this is only for a particular result of the Fourier Series where the integral includes pi. Thank you for your answer though Simon.
     
  5. Jun 12, 2014 #4

    Simon Bridge

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    No worries, and well done.
    Thanks for sharing too.
    :)
     
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