36:
a: \(sinx=-\dfrac{1}{2}\)
=>\(sinx=sin\left(-\dfrac{\Omega}{6}\right)\)
=>Sai
b: \(sinx=sin\left(-\dfrac{\Omega}{6}\right)\)
=>\(\left[{}\begin{matrix}x=-\dfrac{\Omega}{6}+k2\Omega\\x=\Omega+\dfrac{\Omega}{6}+k2\Omega=\dfrac{7}{6}\Omega+k2\Omega\end{matrix}\right.\)
=>Đúng
c: Đúng
d: \(x\in\left(-\Omega;\Omega\right)\)
=>\(\left[{}\begin{matrix}2k-\dfrac{1}{6}\in\left(-1;1\right)\\2k+\dfrac{7}{6}\in\left(-1;1\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2k\in\left(-\dfrac{5}{6};\dfrac{7}{6}\right)\\2k\in\left(-\dfrac{13}{6};-\dfrac{1}{6}\right)\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}k\in\left(-\dfrac{5}{12};\dfrac{7}{12}\right)\\k\in\left(-\dfrac{13}{12};-\dfrac{1}{12}\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}k=0\\k=-1\end{matrix}\right.\)
=>Có hai nghiệm
=>Đúng
37:
a: \(2\cdot sinx=\sqrt{2}\)
=>\(sinx=\dfrac{\sqrt{2}}{2}=sin\left(\dfrac{\Omega}{4}\right)\)
=>Đúng
b: \(sinx=sin\left(\dfrac{\Omega}{4}\right)\)
=>\(\left[{}\begin{matrix}x=\dfrac{\Omega}{4}+k2\Omega\\x=\Omega-\dfrac{\Omega}{4}+k2\Omega=\dfrac{3}{4}\Omega+k2\Omega\end{matrix}\right.\)
=>Sai
c: Đúng
d: \(x\in\left(-\dfrac{\Omega}{2};\dfrac{\Omega}{2}\right)\)
=>\(\left[{}\begin{matrix}\dfrac{\Omega}{4}+k2\Omega\in\left(-\dfrac{\Omega}{2};\dfrac{\Omega}{2}\right)\\\dfrac{3}{4}\Omega+k2\Omega\in\left(-\dfrac{\Omega}{2};\dfrac{\Omega}{2}\right)\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}2k+\dfrac{1}{4}\in\left(-\dfrac{1}{2};\dfrac{1}{2}\right)\\2k+\dfrac{3}{4}\in\left(-\dfrac{1}{2};\dfrac{1}{2}\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2k\in\left(-\dfrac{3}{4};\dfrac{1}{4}\right)\\2k\in\left(-\dfrac{5}{4};-\dfrac{1}{4}\right)\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}k\in\left(-\dfrac{3}{8};\dfrac{1}{8}\right)\\k\in\left(-\dfrac{5}{8};-\dfrac{1}{8}\right)\end{matrix}\right.\Leftrightarrow k=0\)
=>Có 1 nghiệm
=>Sai
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