## Trigonometry 7th Edition

$\dfrac{\sqrt3}{2}$
Substitute $\frac{\pi}{6}$ to $x$ to obtain: $\sin{(2x)}= \sin{2(\frac{\pi}{6})}=\sin{(\frac{\pi}{3})}$ $\dfrac{\pi}{3}$ is a special angle whose sine value is $\dfrac{\sqrt{3}}{2}$. Thus, when $x=\frac{\pi}{6}$, $\sin{(2x)} = \dfrac{\sqrt3}{2}$