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Math Help - Rewriting cos

  1. #1
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    Rewriting cos

    How would I rewrite cos3theta in terms of costheta any help would be much appreciated!
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  2. #2
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    Quote Originally Posted by abc10 View Post
    How would I rewrite cos3theta in terms of costheta any help would be much appreciated!
    \cos(2x+x)=\cos(2x)\cos(x) - \sin(2x)\sin(x)=\cdots
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  3. #3
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    Quote Originally Posted by abc10 View Post
    How would I rewrite cos3\theta in terms of cos\theta any help would be much appreciated!
    Cos3\theta=Cos(2\theta+\theta)


    Cos(A+B)=CosACosB-SinASinB


    \Rightarrow\ Cos3\theta=Cos2\theta\ Cos\theta-Sin2\theta\ Sin\theta


    Cos2A=Cos^2A-Sin^2A

    Sin2A=2SinACosA

    Sin^2A=1-Cos^2A


    \Rightarrow\ Cos3\theta=\left[Cos^2\theta-Sin^2\theta\right]Cos\theta-2Sin\theta\ Cos\theta\ Sin\theta

    =Cos^3\theta-\left(1-Cos^2\theta\right)Cos\theta-2\left(1-Cos^2\theta\right)Cos\theta
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    You guys rock!
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