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Math Help - Finding the sum of a trigonometric series?

  1. #1
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    Finding the sum of a trigonometric series?

    Find the sum of the series Finding the sum of a trigonometric series?-trig-series.jpg. You must calculate the sum of this series only by multiplying through by Finding the sum of a trigonometric series?-2sinxover2.jpg

    Now I've heard of finding the sum of a trig series by finding real and imaginary parts etc., but I have no idea how to do it this way.

    any help or advice is hugely appreciated!

    thank you
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  2. #2
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    Re: Finding the sum of a trigonometric series?

    Make repeated use of the trig identity

    \sin(A)-\sin(B)=2\cos\left(\frac{A+B}{2}\right)\sin \left( \frac{A-B}{2}\right).
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  3. #3
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    Re: Finding the sum of a trigonometric series?

    Quote Originally Posted by BobP View Post
    Make repeated use of the trig identity

    \sin(A)-\sin(B)=2\cos\left(\frac{A+B}{2}\right)\sin \left( \frac{A-B}{2}\right).
    Hi Bob, thank you for that

    could you possibly explain this further? would I do this by substituting?
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  4. #4
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    Re: Finding the sum of a trigonometric series?

    Having multiplied throughout by 2\sin(x/2), consider a general term in the resulting series, 2\cos(kx)\sin(x/2).

    Use the trig identity to break this into two terms.

    Apply this to each term of your series in turn, when you've done this, you should find that there is a whole lot of cancellation, after which you need to use the trig identity again.
    Don't forget to divide the resulting expression by 2\sin(x/2), .
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