Answer
$\dfrac{\sqrt{3}}{2}$
Work Step by Step
RECALL:
(1)The reference angle of a given angle is equal to the smallest acute angle that the terminal side makes with the x-axis.
(2) Based on the location of the terminal side of an angle $\theta$, the reference angle can be found using the formula:
(i) Quadrant I: $\theta$
(ii) Quadrant II: $\pi-\theta$
(iii) Quadrant III: $\theta-\pi$
(iv) Quadrant IV: $2\pi-\theta$
The given angle is in Quadrant II I so its reference angle is:
$=\pi - \dfrac{2\pi}{3}
\\=\dfrac{\pi}{3}$
The value of sine in Quadrant II is positive.
Thus,
$\sin{\frac{2\pi}{3}} = \sin{\frac{\pi}{3}}$
$\dfrac{\pi}{3}$ is a special angle whose sine value is $\dfrac{\sqrt{3}}{2}$.
Thus,
$\sin{\dfrac{2\pi}{3}}=\sin{\dfrac{\pi}{3}}=\dfrac{\sqrt{3}}{2}$
