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Math Help - Periodic functions and Fourier Series

  1. #1
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    Periodic functions and Fourier Series

    I'm looking at some examples that I have and I follow them until I get to the result where something like -2*(-1 + cos(Pi*m)) / Pi*m^2
    is simplified to -2/Pi*m^2 ((-1)^m - 1)

    Why does the cos(Pi*m) turn into (-1)^m?
    And if this was sin instead what would happen?

    I may be forgetting some old simple rule that I should have learnt
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  2. #2
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    Quote Originally Posted by Unoticed View Post
    I'm looking at some examples that I have and I follow them until I get to the result where something like -2*(-1 + cos(Pi*m)) / Pi*m^2
    is simplified to -2/Pi*m^2 ((-1)^m - 1)

    Why does the cos(Pi*m) turn into (-1)^m?
    And if this was sin instead what would happen?

    I may be forgetting some old simple rule that I should have learnt
    \cos 0 = 1, \, \cos \pi = -1, \, \cos 2\pi = 1, \, \cos 3 \pi = -1, \, .... See the pattern?

    \sin m \pi = 0 as your old forgotten friend the unit circle will gladly tell you if you catch up for a chat ......
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  3. #3
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    lol thanks, I realised shortly after I made the post.
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