## virtus Group Title express sin 3theta in terms of sin theta 2 years ago 2 years ago

1. Zed
2. Zed

It's located under Double-, triple-, and half-angle formulae

3. malevolence19

$\sin(3 \phi)=\frac{e^{3i \phi}-e^{-3i \phi}}{2i}$ Then use: $e^{3i \phi}=(e^{i \phi})^3; e^{i \phi}=\cos(\phi)+i \sin(\phi)$ Then set the real part equal.

4. virtus

thanks but i do not really understand the working out

5. rivermaker

If you know the formula for $\sin (A+B)$ then you can derive the formula for $\sin 2A = \sin (A + A)$ and $\sin 3A = \sin (A + 2A)$