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Simplify sin3θ

  1. Mar 25, 2010 #1
    1. The problem statement, all variables and given/known data
    Simplify Sin[3θ] (no double angles)

    2. Relevant equations
    Sin[3θ]=Sin[θ+2θ]
    Sin[α + β] = Sin[α] Cos[β] + Cos[α] Sin[β]
    Sin[3θ] = 3sinθ - 4sin^3 θ
    Cos2θ = 1-2Sin^2θ

    3. The attempt at a solution
    Sin[3θ] = sin[θ+2θ]
    Sin[θ+2θ] = Sinθ Cos2θ + Cosθ Sin2θ
    Sinθ Cos2θ + Cosθ Sin2θ = Sinθ (1-2Sin^2θ) + Cosθ Sin2θ
    =Sinθ - 2Sin^3θ + Cosθ Sin2θ This is where i get lost...I know it should end up being
    = (3sinθ - 4sin^3 θ) but i cannot figure out how to get there. I don't know whether I just dont have the formula i need or what.
     
  2. jcsd
  3. Mar 25, 2010 #2

    rock.freak667

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    Homework Helper

    Sin2θ = 2sinθcosθ, remember that one?
     
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