Question

GPT: \(\sin2x=\dfrac{-\sqrt{2}}{2}\)

Answer 1

\(\sin2x=\dfrac{-\sqrt{2}}{2}\Leftrightarrow\sin2x=-\dfrac{\pi}{4}\)

\(\Leftrightarrow\left[{}\begin{matrix}2x=-\dfrac{\pi}{4}+k2\pi\\2x=\pi-\left(-\dfrac{\pi}{4}\right)+k2\pi\end{matrix}\right.=\left[{}\begin{matrix}x=-\dfrac{\pi}{8}+k\pi\\x=\dfrac{5\pi}{8}+k\pi\end{matrix}\right.\left(k\in Z\right)\)