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Adding cos

  1. Sep 4, 2014 #1
    1. The problem statement, all variables and given/known data
    Calculate
    [itex] cos\frac{2\pi}{2n+1} + cos\frac{4\pi}{2n+1} + cos\frac{6\pi}{2n+1} + ... + cos\frac{2n\pi}{2n+1} [/itex]


    2. Relevant equations
    Complex equations, maybe :p

    3. The attempt at a solution
    Let's say
    [itex] z^{2n+1} = 1 [/itex]
    The sum is equivalent to the sum of the real even roots of the equation above. That's it. Ideas?
     
  2. jcsd
  3. Sep 4, 2014 #2

    Ray Vickson

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    What are YOUR ideas?
     
  4. Sep 7, 2014 #3
    Those were basically my ideas, I just didn't write down my complete attempt at the solution, sorry. But I could find out what was missing in my resolution xD Thanks, Ray
     
  5. Sep 7, 2014 #4

    vela

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    How are we supposed to see what's missing if you don't show us what you did?
     
  6. Sep 8, 2014 #5

    HallsofIvy

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    You mention that, in the complex plane, the given arguments lie equally spaced about the unit circle so did you consider using [itex]cos(z)=(e^{iz}+ e^{-iz})/2[/itex]?
     
  7. Sep 8, 2014 #6
    Actually, I didn't solve it this way, but nice one though! Thanks, hallsoflvy
     
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