Question

Rewrite the expression in terms of the given angle's reference angle; then evaluate the result. Write the exact answer. Do not round.sin1113

Answer 1

Rewrite the angle inside the expression as:

`(11\pi)/(3)=4\pi-(\pi)/(3)`

Apply sine function on both sides and use the identity sin(A-B) = sin A cos B - cos A sin B.

`\begin{gathered} \sin ((11\pi)/(3))=\sin (4\pi-(\pi)/(3)) \\ =\sin 4\pi\cos (\pi)/(3)-\cos 4\pi\sin (\pi)/(3) \\ =0\cdot\cos (\pi)/(3)-1\cdot\frac{\sqrt[]{3}}{2} \\ =-\frac{\sqrt[]{3}}{2} \end{gathered}`