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:

$\frac{11\pi}{3}=4\pi-\frac{\pi}{3}$

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

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