How to calculate this: Given sin θ = 3/4, 0º < θ < 90º, what's the value of sin (4θ)? Thanks
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Hello nvwxgn Originally Posted by nvwxgn How to calculate this: Given sin θ = 3/4, 0º < θ < 90º, what's the value of sin (4θ)? Thanks Use Pythagoras' Theorem to find $\displaystyle \cos\theta$; then use the formula for $\displaystyle \sin4\theta$ that you'll find on this page. Can you complete it now? Grandad
Originally Posted by nvwxgn How to calculate this: Given sin θ = 3/4, 0º < θ < 90º, what's the value of sin (4θ)? Can you show that $\displaystyle \sin (4\theta ) = 4\sin (\theta )\cos (\theta )\left[ {\cos ^2 (\theta ) - \sin ^2 (\theta )} \right]?$
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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