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Math Help - Express in terms of theta

  1. #1
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    Express in terms of theta

    I have to express: cos 6θ and sin 6θ in terms of sinθ and cosθ.

    I tried to do it using Demoivre's formula but it looks horribly wrong
    I got: (cosθ + sinθ)^6

    any assistance would be appreciated.
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  2. #2
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    Quote Originally Posted by blackhug View Post
    I have to express: cos 6θ and sin 6θ in terms of sinθ and cosθ.

    I tried to do it using Demoivre's formula but it looks horribly wrong
    I got: (cosθ + sinθ)^6

    any assistance would be appreciated.
    De Moivre's formula says that \cos6\theta + i\sin6\theta = (\cos\theta+i\sin\theta)^6. Expand the right side by the binomial theorem. Then take the real part to get \cos6\theta = \cos^6\theta - 15\cos^4\theta\sin^2\theta + 15\cos^2\theta\sin^4\theta - \sin^6\theta. Taking the imaginary part yields a similar formula for \sin6\theta.
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