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Identity problem

  1. Jan 25, 2010 #1
    Hi friends,

    I am not able to understand how the below shown identity becomes (-1) power v cosθ.

    cos(vπ − θ ) = cos vπ cos θ + sin vπ sin θ = (−1)power v cos θ

    ==> (-1)vcos θ

    Please help me understand this basic problem.

    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Jan 25, 2010 #2


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    Homework Helper

    You must mean v is an integer. So v=...-2,-1,0,1,2... Start working out sin(1*pi), sin(2*pi), sin(3*pi) ... and cos(1*pi), cos(2*pi), cos(3*pi) ... Do you see a pattern?
  4. Jan 25, 2010 #3
    Thank you very much, I understand now.

    cos vπ cos θ + sin vπ sin θ

    Since sin n*pi is always zero, we can omit this.

    v=0 : cos(0π)cosθ + sin0 = cosθ
    v=1 : cos(1π)cosθ + 0 = -1 cosθ
    v=2 : cos(2π)cosθ + 0 = 1 cosθ
    v=3 : cos(3π)cosθ + 0 = -1 cosθ

    so in general we can write it as (-1)to power v cos θ

    Thank you very much.
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