- LG a
- LG b
- LG c
- LG d
- LG e
- LG f
Giải các phương trình sau:
LG a
\[\sin \left[ {3x - {\pi \over 6}} \right] = {{\sqrt 3 } \over 2}\]
Lời giải chi tiết:
\[\begin{array}{l}
\sin \left[ {3x - \frac{\pi }{6}} \right] = \frac{{\sqrt 3 }}{2}\\
\Leftrightarrow \sin \left[ {3x - \frac{\pi }{6}} \right] = \sin \frac{\pi }{3}\\
\Leftrightarrow \left[ \begin{array}{l}
3x - \frac{\pi }{6} = \frac{\pi }{3} + k2\pi \\
3x - \frac{\pi }{6} = \pi - \frac{\pi }{3} + k2\pi
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
3x = \frac{\pi }{2} + k2\pi \\
3x = \frac{{5\pi }}{6} + k2\pi
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \frac{\pi }{6} + \frac{{k2\pi }}{3}\\
x = \frac{{5\pi }}{{18}} + \frac{{k2\pi }}{3}
\end{array} \right.
\end{array}\]
LG b
\[\sin \left[ {3x - 2} \right] = - 1\]
Lời giải chi tiết:
\[\begin{array}{l}
\sin \left[ {3x - 2} \right] = - 1\\
\Leftrightarrow 3x - 2 = - \frac{\pi }{2} + k2\pi \\
\Leftrightarrow 3x = 2 - \frac{\pi }{2} + k2\pi \\
\Leftrightarrow x = \frac{2}{3} - \frac{\pi }{6} + \frac{{k2\pi }}{3}
\end{array}\]
LG c
\[\sqrt 2 \cos \left[ {2x - {\pi \over 5}} \right] = 1\]
Lời giải chi tiết:
\[\begin{array}{l}
\sqrt 2 \cos \left[ {2x - \frac{\pi }{5}} \right] = 1\\
\Leftrightarrow \cos \left[ {2x - \frac{\pi }{5}} \right] = \frac{1}{{\sqrt 2 }}\\
\Leftrightarrow \cos \left[ {2x - \frac{\pi }{5}} \right] = \cos \frac{\pi }{4}\\
\Leftrightarrow \left[ \begin{array}{l}
2x - \frac{\pi }{5} = \frac{\pi }{4} + k2\pi \\
2x - \frac{\pi }{5} = - \frac{\pi }{4} + k2\pi
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
2x = \frac{{9\pi }}{{20}} + k2\pi \\
2x = - \frac{\pi }{{20}} + k2\pi
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \frac{{9\pi }}{{40}} + k\pi \\
x = - \frac{\pi }{{40}} + k\pi
\end{array} \right.
\end{array}\]
LG d
\[\cos \left[ {3x - {{15}^o}} \right] = \cos {150^o}\]
Lời giải chi tiết:
\[\begin{array}{l}
\cos \left[ {3x - {{15}^0}} \right] = \cos {150^0}\\
\Leftrightarrow \left[ \begin{array}{l}
3x - {15^0} = {150^0} + k{360^0}\\
3x - {15^0} = - {150^0} + k{360^0}
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
3x = {165^0} + k{360^0}\\
3x = - {135^0} + k{360^0}
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = {55^0} + k{120^0}\\
x = - {45^0} + k{120^0}
\end{array} \right.
\end{array}\]
LG e
\[\tan \left[ {2x +3} \right] = \tan {\pi \over 3}\]
Lời giải chi tiết:
\[\begin{array}{l}
\tan \left[ {2x + 3} \right] = \tan \frac{\pi }{3}\\
\Leftrightarrow 2x + 3 = \frac{\pi }{3} + k\pi \\
\Leftrightarrow 2x = \frac{\pi }{3} - 3 + k\pi \\
\Leftrightarrow x = \frac{\pi }{6} - \frac{3}{2} + \frac{{k\pi }}{2}
\end{array}\]
LG f
\[\cot \left[ {{{45}^o} - x} \right] = {{\sqrt 3 } \over 3}\]
Lời giải chi tiết:
\[\begin{array}{l}
\cot \left[ {{{45}^0} - x} \right] = \frac{{\sqrt 3 }}{3}\\
\Leftrightarrow \cot \left[ {{{45}^0} - x} \right] = \cot {60^0}\\
\Leftrightarrow {45^0} - x = {60^0} + k{180^0}\\
\Leftrightarrow x = - {15^0} - k{180^0}
\end{array}\]