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Math Help - Angle multiplication

  1. #1
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    Angle multiplication

    How to calculate this:

    Given sin θ = 3/4, 0 < θ < 90, what's the value of sin (4θ)?

    Thanks
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  2. #2
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    Hello nvwxgn
    Quote Originally Posted by nvwxgn View Post
    How to calculate this:

    Given sin θ = 3/4, 0 < θ < 90, what's the value of sin (4θ)?

    Thanks
    Use Pythagoras' Theorem to find \cos\theta; then use the formula for \sin4\theta that you'll find on this page.

    Can you complete it now?

    Grandad

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  3. #3
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    Quote Originally Posted by nvwxgn View Post
    How to calculate this:
    Given sin θ = 3/4, 0 < θ < 90, what's the value of sin (4θ)?
    Can you show that \sin (4\theta ) = 4\sin (\theta )\cos (\theta )\left[ {\cos ^2 (\theta ) - \sin ^2 (\theta )} \right]?
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  4. #4
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    Figured it out, using complex numbers:

    (cos θ + isin θ)^4
    Isolating sin and making the substitutions, we have -3sqrt(7)/32, which agrees with my calculator.
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