Toán Lớp 11: 1.sin x =1/2
2.sin(x+30 độ)=1/2
3.sin2x =căn2 /2
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Toán Lớp 11: 1.sin x =1/2
2.sin(x+30 độ)=1/2
3.sin2x =căn2 /2
Comments ( 1 )
1,\\
\left[ \begin{array}{l}
x = \dfrac{\pi }{6} + k2\pi \\
x = \dfrac{{5\pi }}{6} + k2\pi
\end{array} \right.\,\,\,\left( {k \in Z} \right)\\
2,\\
\left[ \begin{array}{l}
x = k.360^\circ \\
x = 120^\circ + k.360^\circ
\end{array} \right.\,\,\,\left( {k \in Z} \right)\\
3,\\
\left[ \begin{array}{l}
x = \dfrac{\pi }{8} + k\pi \\
x = \dfrac{{3\pi }}{8} + k\pi
\end{array} \right.\,\,\,\,\left( {k \in Z} \right)
\end{array}\)
1,\\
\sin x = \dfrac{1}{2}\\
\Leftrightarrow \sin x = \sin \dfrac{\pi }{6}\\
\Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{\pi }{6} + k2\pi \\
x = \pi – \dfrac{\pi }{6} + k2\pi
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{\pi }{6} + k2\pi \\
x = \dfrac{{5\pi }}{6} + k2\pi
\end{array} \right.\,\,\,\left( {k \in Z} \right)\\
2,\\
\sin \left( {x + 30^\circ } \right) = \dfrac{1}{2}\\
\Leftrightarrow \sin \left( {x + 30^\circ } \right) = \sin 30^\circ \\
\Leftrightarrow \left[ \begin{array}{l}
x + 30^\circ = 30^\circ + k.360^\circ \\
x + 30^\circ = 180^\circ – 30^\circ + k.360^\circ
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = k.360^\circ \\
x = 120^\circ + k.360^\circ
\end{array} \right.\,\,\,\left( {k \in Z} \right)\\
3,\\
\sin 2x = \dfrac{{\sqrt 2 }}{2}\\
\Leftrightarrow \sin 2x = \sin \dfrac{\pi }{4}\\
\Leftrightarrow \left[ \begin{array}{l}
2x = \dfrac{\pi }{4} + k2\pi \\
2x = \pi – \dfrac{\pi }{4} + k2\pi
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
2x = \dfrac{\pi }{4} + k2\pi \\
2x = \dfrac{{3\pi }}{4} + k2\pi
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{\pi }{8} + k\pi \\
x = \dfrac{{3\pi }}{8} + k\pi
\end{array} \right.\,\,\,\,\left( {k \in Z} \right)
\end{array}\)