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:
\(\begin{array}{l}
\cot \left( {{{45}^0} - x} \right) = \frac{{\sqrt 3 }}{3}\\
\Leftrightarrow \cot \left( {{{45}^0} - x} \right) = \cot {60^0}\\
\Leftrightarrow {45^0} - x = {60^0} + k{180^0}\\
\Leftrightarrow x = - {15^0} - k{180^0}
\end{array}\)
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