\(\Leftrightarrow sin7x=-\dfrac{1}{4}\)
\(\Leftrightarrow\left[{}\begin{matrix}7x=arcsin\left(-\dfrac{1}{4}\right)+k2\pi\\7x=\pi-arcsin\left(-\dfrac{1}{4}\right)+k2\pi\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{7}arcsin\left(-\dfrac{1}{4}\right)+\dfrac{k2\pi}{7}\\x=\dfrac{\pi}{7}-\dfrac{1}{7}arcsin\left(-\dfrac{1}{4}\right)+\dfrac{k2\pi}{7}\end{matrix}\right.\) (\(k\in Z\))
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