Answer
$-\dfrac{\sqrt3}{2}$
Work Step by Step
$\dfrac{4\pi}{3}$ is an angle in Quadrant III.
The reference angle of an angle in Quadrant III can be found using the formula $\theta - \pi$.
Thus, the reference angle of $\dfrac{4\pi}{3}$ is:
$\dfrac{4\pi}{3} - \pi = \dfrac{4\pi}{3}-\dfrac{3\pi}{3} = \dfrac{\pi}{3}$
$\dfrac{\pi}{3}$ is a special angle whose sine value is $\dfrac{\sqrt3}{2}$. However, since $\dfrac{4\pi}{3}$ is in Quadrant III, then its sine value is negative.
Thus,
$\sin{(\frac{4\pi}{3})}=-\frac{\sqrt3}{2}$
