Toán Phương trình sin2x = – (1/2) có bao nhiêu nghiệm thỏa 0 < x < pi 18/09/2021 By Audrey Phương trình sin2x = – (1/2) có bao nhiêu nghiệm thỏa 0 < x < pi
$\begin{array}{l} \sin 2x = – \frac{1}{2} = \sin \left( { – \frac{\pi }{6}} \right)\\ \Leftrightarrow \left[ \begin{array}{l} 2x = – \frac{\pi }{6} + k2\pi \\ 2x = \frac{{7\pi }}{6} + k2\pi \end{array} \right.\\ \Leftrightarrow \left[ \begin{array}{l} x = – \frac{\pi }{{12}} + k\pi \\ x = \frac{{7\pi }}{{12}} + k\pi \end{array} \right.\\ Ma\,0 < x < \pi \Leftrightarrow \left[ \begin{array}{l} 0 < - \frac{\pi }{{12}} + k\pi < \pi \\ 0 < \frac{{7\pi }}{{12}} + k\pi < \pi \end{array} \right. \Leftrightarrow \left[ \begin{array}{l} k = 1\\ k = 0 \end{array} \right.\\ Co\,2\,nghiem. \end{array}$ Trả lời
$\begin{array}{l}
\sin 2x = – \frac{1}{2} = \sin \left( { – \frac{\pi }{6}} \right)\\
\Leftrightarrow \left[ \begin{array}{l}
2x = – \frac{\pi }{6} + k2\pi \\
2x = \frac{{7\pi }}{6} + k2\pi
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = – \frac{\pi }{{12}} + k\pi \\
x = \frac{{7\pi }}{{12}} + k\pi
\end{array} \right.\\
Ma\,0 < x < \pi \Leftrightarrow \left[ \begin{array}{l} 0 < - \frac{\pi }{{12}} + k\pi < \pi \\ 0 < \frac{{7\pi }}{{12}} + k\pi < \pi \end{array} \right. \Leftrightarrow \left[ \begin{array}{l} k = 1\\ k = 0 \end{array} \right.\\ Co\,2\,nghiem. \end{array}$