Question

giúp mình giải câu này với ạ!
3.Sin(2x+\(\dfrac{π}{3}\)) = 2

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Answer 1

\(\Leftrightarrow sin\left(2x+\frac{\pi}{3}\right)=\frac{2}{3}\)

\(\Rightarrow\left[{}\begin{matrix}2x+\frac{\pi}{3}=arcsin\left(\frac{2}{3}\right)+k2\pi\\2x+\frac{\pi}{3}=\pi-arcsin\left(\frac{2}{3}\right)+k2\pi\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=-\frac{\pi}{6}+\frac{1}{2}arcsin\left(\frac{2}{3}\right)+k\pi\\x=\frac{\pi}{3}-\frac{1}{2}arcsin\left(\frac{2}{3}\right)+k\pi\end{matrix}\right.\)