Question

find the exact value.
sin \frac{4\pi}{3}
type + or -
? \frac{\sqrt{}}{}

Explanation:

Step1: Determine the reference angle

The angle \(\frac{4\pi}{3}\) is in the third quadrant. The reference angle \(\theta_{r}=\frac{4\pi}{3}-\pi=\frac{\pi}{3}\).

Step2: Use the sine function in the third quadrant

In the third quadrant, \(\sin\theta<0\). And \(\sin\frac{\pi}{3}=\frac{\sqrt{3}}{2}\). So \(\sin\frac{4\pi}{3}=-\sin\frac{\pi}{3}\).

Answer:

\(-\frac{\sqrt{3}}{2}\)