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Math Help - Sum of sine and cosine

  1. #1
    Member roshanhero's Avatar
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    Sum of sine and cosine

    What is the formula and how to derive the formula of sina+sin2a+sin3a...........?
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  2. #2
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    Quote Originally Posted by roshanhero View Post
    What is the formula and how to derive the formula of sina+sin2a+sin3a...........?
    Take a look at this Wikipedia article on trigonometric identities. The sum and difference formulas are in there.

    For this problem, start writing out each term as a sum of the previous term and look for a pattern.

    \sin(a)
    \sin(2a)=\sin(a)\cos(a)+ \sin(a)\cos(a)=2\sin(a)\cos(a)
    \sin(3a)=\sin(2a+a)=\sin(2a)\cos(a)+\sin(a)\cos(2a  )

    We already know the sin(2a) though and it isn't hard to find the cos(2a). Every next term can use the previous term to help expand it. Try writing out a few more terms and see what patterns you can find.
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    Member roshanhero's Avatar
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    Tomorrow is my exam and i need this formula pls.......
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    Quote Originally Posted by roshanhero View Post
    Tomorrow is my exam and i need this formula pls.......
    I already gave you a start. Try to see a pattern. On the link I showed you there is a lot of good info about generalizing the sin(n*a) and cos(n*a)
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  5. #5
    Super Member fardeen_gen's Avatar
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    What is the formula and how to derive the formula of sina+sin2a+sin3a...........?
    Jameson already did the groundwork by providing that excellent link. I did some work and here is what I got:

    sin(α) + sin (α + β) + sin (α + 2β) + ... to n terms
    = [sin[α + (n - 1)β/2] . sin(nβ/2)]/sin(β/2)


    This was a general case for which I derived a formula. Things become simpler for the formula which you require as we just need to put β = α and plug into the above formula.
    Last edited by fardeen_gen; December 2nd 2008 at 06:35 AM.
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