Use De Moivre's Thereom To Express Cos3θ Interms

Anonymous

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Use de Moivre's thereom to express cos3θ interms of a) cosθ and sinθ b) cosθ help greatly appreciated, please explain what you are doing so Iunderstand? thanks!

 

Answer No.1

Anonymous

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Cos3θ = cos(2θ+θ)=cos(2θ).cos(θ) - sin(2θ).sin(θ) = (2cos2 (θ) -1) .cos(θ) - 2cosθ.sinθ.sinθ = cosθ( 2cos2 (θ) - 1 - 2 sin2 θ ) = cosθ( 2cos2(θ) - 1 - 2 (1- cos2 θ ) ) = 2cos3 (θ)- cosθ -2 cosθ + cos3θ cos3θ = 4 cos3 (θ)- 3cosθ ANSWER eiθ = cos θ + isinθ (eiθ )3 =(e3 iθ = cos (3θ) + isin(3θ)

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