# Math Help - Angle multiplication

1. ## Angle multiplication

How to calculate this:

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

Thanks

2. 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 $\cos\theta$; then use the formula for $\sin4\theta$ that you'll find on this page.

Can you complete it now?

3. 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 $\sin (4\theta ) = 4\sin (\theta )\cos (\theta )\left[ {\cos ^2 (\theta ) - \sin ^2 (\theta )} \right]?$

4. 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.