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