g) $sin4x=\dfrac{2}{3}$
⇔ \(\left[ \begin{array}{l}4x=arcsin\dfrac{2}{3}+k2\pi\\4x=\pi-arcsin\dfrac{2}{3}+k2\pi\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=\dfrac{1}{4}arcsin(\dfrac{2}{3})+\dfrac{k\pi}{2}\\x=\dfrac{\pi}{4}-\dfrac{1}{4}arcsin(\dfrac{2}{3})+\dfrac{k\pi}{2}\end{array} \right.\) $(k∈\mathbb{Z})$
h) $sin(2x+\dfrac{\pi}{6)}=-\dfrac{3}{2}$
Vì $-1≤sin(2x+\dfrac{\pi}{6})≤1$
Mà $sin(2x+\dfrac{\pi}{6)}=-\dfrac{3}{2}<-1$ nên phương trình vô nghiệm.
i) $2sin2x+\sqrt{2}=0$
⇔ $sin2x=-\dfrac{\sqrt{2}}{2}$
⇔ $sin2x=sin(-\dfrac{\pi}{4})$
⇔ \(\left[ \begin{array}{l}2x=-\dfrac{\pi}{4}+k2\pi\\2x=\pi+\dfrac{\pi}{4}+k2\pi\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=-\dfrac{\pi}{8}+k\pi\\x=\dfrac{5\pi}{8}+k\pi\end{array} \right.\) $(k∈\mathbb{Z})$
