Question

GPT: \(\sin\left(2x+\dfrac{\pi}{4}\right)=-\dfrac{1}{2}\)

Answer 1

Answer 2

\(\sin\left(2x+\dfrac{\pi}{4}\right)=-\dfrac{1}{2}\)

\(\Leftrightarrow\sin\left(2x+\dfrac{\pi}{4}\right)=-\dfrac{\pi}{6}\)

\(\Leftrightarrow\left[{}\begin{matrix}2x+\dfrac{\pi}{4}=-\dfrac{\pi}{6}+k2\pi\\2x+\dfrac{\pi}{4}=\pi-\left(-\dfrac{\pi}{6}\right)+k2\pi\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}2x=-\dfrac{\pi}{6}-\dfrac{\pi}{4}+k2\pi\\2x=\pi+\dfrac{\pi}{6}-\dfrac{\pi}{4}+k2\pi\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=-\dfrac{5\pi}{12}+k2\pi\\2x=\dfrac{11\pi}{12}+k2\pi\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{5\pi}{24}+k\pi\\x=\dfrac{11\pi}{24}+k\pi\end{matrix}\right.\left(k\in Z\right)\)

Answer 3

=)) sẽ chỉ có 1 người trl:vv