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Math Help - Math Proof

  1. #1
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    Math Proof

    One of my teaches gave me this problem as extra credit. Proofs like this were not a pre-requisit for the class so I dont' think he expected anyone to solve it. I don't even know where to get started and when I asked him for a suggestion of where to start he simply replied that he didnt' even know how to do it. Any suggestions of where to start would be helpful.

    Here is the problem. I scanned it and cropped it so it wasn't to big.
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  2. #2
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    These results are both true, but to prove them you probably need to know something about complex numbers. For the first problem, \sin(\omega t + \tfrac{2\pi}Nk) is the imaginary part of e^{i\omega t}z, where z is an Nth root of unity. The result follows from the fact the sum of the Nth roots of unity is 0. This is a good place to start looking for information on this.

    For the second problem, use the trig formula \sin^2\theta = \tfrac12(1-\cos(2\theta)). That will transform the second problem into something looking very much like the first problem (but with cos instead of sin, and 2k instead of k).
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  3. #3
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    I don't get it
    So do i start by substituting that in for N?

    I do understand how the second one relates to the first one with the trig formula though
    Last edited by colbys_11; March 12th 2009 at 08:01 PM.
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  4. #4
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    So after looking at it(the first one) more i think i can simplify it a little bit to make it look like this

    ------->N
    [sin(wt)]Σsin(wt+(2Π/N)K) = 0
    ------->k=1

    so i took out the where k = 0
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