a: sin x=0
=>\(x=k\Omega\)
b: \(sinx=\dfrac{1}{2}\)
=>\(\left[{}\begin{matrix}x=\dfrac{\Omega}{6}+k2\Omega\\x=\Omega-\dfrac{\Omega}{6}+k2\Omega=\dfrac{5}{6}\Omega+k2\Omega\end{matrix}\right.\)
c:
\(sin\left(x+\dfrac{\Omega}{4}\right)=\dfrac{\sqrt{3}}{2}\)
=>\(\left[{}\begin{matrix}x+\dfrac{\Omega}{4}=\dfrac{\Omega}{3}+k2\Omega\\x+\dfrac{\Omega}{4}=\Omega-\dfrac{\Omega}{3}+k2\Omega=\dfrac{2}{3}\Omega+k2\Omega\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=\dfrac{\Omega}{3}+k2\Omega-\dfrac{\Omega}{4}=\dfrac{\Omega}{12}+k2\Omega\\x=\dfrac{2}{3}\Omega-\dfrac{\Omega}{4}+k2\Omega=\dfrac{5}{12}\Omega+k2\Omega\end{matrix}\right.\)
d: \(2\cdot sinx-\sqrt{3}=0\)
=>\(sinx=\dfrac{\sqrt{3}}{2}\)
=>\(\left[{}\begin{matrix}x=\dfrac{\Omega}{3}+k2\Omega\\x=\Omega-\dfrac{\Omega}{3}+k2\Omega=\dfrac{2}{3}\Omega+k2\Omega\end{matrix}\right.\)
e: \(sin\left(\Omega\cdot x\right)=cos\left(\dfrac{\Omega}{3}+\Omega\cdot x\right)\)
=>\(sin\left(\Omega x\right)=sin\left(\dfrac{\Omega}{2}-\dfrac{\Omega}{3}-\Omega x\right)\)
=>\(sin\left(\Omega\cdot x\right)=sin\left(\dfrac{\Omega}{6}-\Omega\cdot x\right)\)
=>\(\left[{}\begin{matrix}\Omega\cdot x=\dfrac{\Omega}{6}-\Omega x+k2\Omega\\\Omega x=\Omega-\dfrac{\Omega}{6}+\Omega x+k2\Omega=\dfrac{5}{6}\Omega+\Omega x+k2\Omega\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}2\Omega\cdot x=\dfrac{\Omega}{6}+k2\Omega\\0=\dfrac{5}{6}\Omega+k2\Omega\left(loại\right)\end{matrix}\right.\Leftrightarrow x=\dfrac{1}{12}+2k\)
f: \(sin\left(2x+30^0\right)=\dfrac{\sqrt{3}}{2}\)
=>\(\left[{}\begin{matrix}2x+30^0=60^0+k\cdot360^0\\2x+30^0=180^0-60^0+k\cdot360^0=120^0+k\cdot360^0\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}2x=30^0+k\cdot360^0\\2x=90^0+k\cdot360^0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=15^0+k\cdot180^0\\x=45^0+k\cdot180^0\end{matrix}\right.\)
i: \(\sqrt{3}\cdot sin2x-cos2x=2\)
=>\(\dfrac{\sqrt{3}}{2}\cdot sin2x-\dfrac{1}{2}\cdot cos2x=1\)
=>\(sin\left(2x-\dfrac{\Omega}{6}\right)=1\)
=>\(2x-\dfrac{\Omega}{6}=\dfrac{\Omega}{2}+k2\Omega\)
=>\(2x=\dfrac{4}{6}\Omega+k2\Omega=\dfrac{2}{3}\Omega+k2\Omega\)
=>\(x=\dfrac{1}{3}\Omega+k\Omega\)
k: \(2\cdot sin^2x-3\cdot sinx+1=0\)
=>\(\left(2\cdot sinx-1\right)\left(sinx-1\right)=0\)
=>\(\left[{}\begin{matrix}sinx=\dfrac{1}{2}\\sinx=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\Omega}{6}+k2\Omega\\x=\Omega-\dfrac{\Omega}{6}+k2\Omega=\dfrac{5}{6}\Omega+k2\Omega\\x=\dfrac{\Omega}{2}+k2\Omega\end{matrix}\right.\)
l: \(cos2x+5\cdot sinx-4=0\)
=>\(1-2\cdot sin^2x+5\cdot sinx-4=0\)
=>\(-2\cdot sin^2x+5\cdot sinx-3=0\)
=>\(\left(2sinx-3\right)\left(sinx-1\right)=0\)
=>\(\left[{}\begin{matrix}sinx=\dfrac{3}{2}\left(loại\right)\\sinx=1\left(nhận\right)\end{matrix}\right.\)
=>\(sinx=1\)
=>\(x=\dfrac{\Omega}{2}+k2\Omega\)
