Question

Evaluate the sine of the angle $0 = 4\pi \div 3$0 is fada

Answer 1

By Compound Angles Theorem,

$\begin{gathered} \sin (\frac{4\pi}{3})=\sin (\frac{2\pi}{3}+\frac{2\pi}{3})=2\sin (\frac{2\pi}{3})\cos (\frac{2\pi}{3})=2(\frac{\sqrt[]{3}}{2})(-\frac{1}{2})=-\frac{\sqrt[]{3}}{2} \\ \end{gathered}$

Recall:

$\begin{gathered} \sin (\frac{2\pi}{3})=\frac{\sqrt[]{3}}{2} \\ \\ \cos (\frac{2\pi}{3})=-\frac{1}{2} \end{gathered}$

Hence, the correct answer is

$-\frac{\sqrt[]{3}}{2}$