Evaluate the sine of the angle 0 = 4\pi / 30 is fada

Question

Evaluate the sine of the angle
`0 = 4\pi / 3`0 is fada

Answer 1

By Compound Angles Theorem,

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

Recall:

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

Hence, the correct answer is

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