Tất cả k dưới đây là \(k\in Z\)
a.
\(2sinx=-\sqrt{2}\)
\(\Leftrightarrow sinx=-\dfrac{\sqrt{2}}{2}\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{\pi}{4}+k2\pi\\x=\dfrac{5\pi}{4}+k2\pi\end{matrix}\right.\)
b.
\(sin\left(x-2\right)=\dfrac{2}{3}\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=arcsin\left(\dfrac{2}{3}\right)+k2\pi\\x-2=\pi-arcsin\left(\dfrac{2}{3}\right)+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2+arcsin\left(\dfrac{2}{3}\right)+k2\pi\\x=2+\pi-arcsin\left(\dfrac{2}{3}\right)+k2\pi\end{matrix}\right.\)
c.
\(sin\left(2x-\dfrac{\pi}{5}\right)=sin\left(\dfrac{\pi}{5}+x\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-\dfrac{\pi}{5}=\dfrac{\pi}{5}+x+k2\pi\\2x-\dfrac{\pi}{5}=\dfrac{4\pi}{5}-x+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{2\pi}{5}+k2\pi\\x=\dfrac{\pi}{3}+\dfrac{k2\pi}{3}\end{matrix}\right.\)
