Ptrinh đã cho tương đương vs
$\sin \left( 3x + \dfrac{\pi}{6} \right) = \dfrac{1}{2}$
$<-> \sin \left( 3x + \dfrac{\pi}{6} \right) = \sin \left( \dfrac{\pi}{6} \right)$
$<-> 3x + \dfrac{\pi}{6} = \dfrac{\pi}{6} + 2k\pi$ hoặc $3x + \dfrac{\pi}{6} = \dfrac{5\pi}{6} + 2k\pi$
$<-> x = \dfrac{2k\pi}{3}$ hoặc $x = \dfrac{2\pi}{9} + \dfrac{2k\pi}{3}$
Do $x \in \left( 0 , \dfrac{\pi}{2} \right)$ nên
$x = \dfrac{2\pi}{9}$
Vậy $S = \left\{ \dfrac{2\pi}{9} \right\}$.
