1.
c, \(sin\left(\dfrac{\pi}{3}-x\right)=-\dfrac{1}{4}\)
\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{\pi}{3}-x=arcsin\left(-\dfrac{1}{4}\right)+k.360^o\\\dfrac{\pi}{3}-x=\pi-arcsin\left(-\dfrac{1}{4}\right)+k.360^o\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{3}-arcsin\left(-\dfrac{1}{4}\right)+k.360^o\\x=-\dfrac{2\pi}{3}+arcsin\left(-\dfrac{1}{4}\right)+k.360^o\end{matrix}\right.\)
d, \(sin4x=\dfrac{2}{3}\)
\(\Leftrightarrow\left[{}\begin{matrix}4x=arcsin\dfrac{2}{3}+k2\pi\\4x=\pi-arcsin\dfrac{2}{3}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{4}arcsin\dfrac{2}{3}+\dfrac{k\pi}{2}\\x=\dfrac{\pi}{4}-\dfrac{1}{4}arcsin\dfrac{2}{3}+\dfrac{k\pi}{2}\end{matrix}\right.\)
1.
e, \(2sin2x+\sqrt{2}=0\)
\(\Leftrightarrow sin2x=-\dfrac{\sqrt{2}}{2}\)
\(\Leftrightarrow sin2x=sin\left(-\dfrac{\pi}{4}\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}2x=-\dfrac{\pi}{4}+k2\pi\\2x=\dfrac{5\pi}{4}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{\pi}{8}+k\pi\\x=\dfrac{5\pi}{8}+k\pi\end{matrix}\right.\)
1.
f, \(sin\left(3x+\dfrac{\pi}{4}\right)=sin\left(x-\dfrac{\pi}{6}\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}3x+\dfrac{\pi}{4}=x-\dfrac{\pi}{6}+k2\pi\\3x+\dfrac{\pi}{4}=-x+\dfrac{7\pi}{6}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{5\pi}{24}+k\pi\\x=\dfrac{11\pi}{48}+\dfrac{k\pi}{2}\end{matrix}\right.\)
2.
d, \(2cos\left(\dfrac{x}{4}+20^o\right)=-\sqrt{3}\)
\(\Leftrightarrow cos\left(\dfrac{x}{4}+20^o\right)=-\dfrac{\sqrt{3}}{2}\)
\(\Leftrightarrow cos\left(\dfrac{x}{4}+20^o\right)=cos150^o\)
\(\Leftrightarrow\dfrac{x}{4}+20^o=\pm150^o+k.360^o\)
\(\Leftrightarrow\left[{}\begin{matrix}x=520^o+k.360^o\\x=-680^o+k.360^o\end{matrix}\right.\)
2.
f, \(cos\left(2x+\dfrac{\pi}{6}\right)+sin3x=0\)
\(\Leftrightarrow cos\left(2x+\dfrac{\pi}{6}\right)+cos\left(3x-\dfrac{\pi}{2}\right)=0\)
\(\Leftrightarrow2cos\left(\dfrac{5x}{2}-\dfrac{\pi}{6}\right).cos\left(-\dfrac{x}{2}+\dfrac{\pi}{3}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cos\left(\dfrac{5x}{2}-\dfrac{\pi}{6}\right)=0\\cos\left(-\dfrac{x}{2}+\dfrac{\pi}{3}\right)=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{5x}{2}-\dfrac{\pi}{6}=\dfrac{\pi}{2}+k\pi\\-\dfrac{x}{2}+\dfrac{\pi}{3}=\dfrac{\pi}{2}+k\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{4\pi}{15}+k2\pi\\x=-\dfrac{\pi}{3}+k2\pi\end{matrix}\right.\)
1.
a, \(sin\left(2x+\dfrac{\pi}{6}\right)=-\dfrac{3}{2}< -1\Rightarrow\) phương trình vô nghiệm.
b, \(sin\left(x+20^o\right)=\dfrac{\sqrt{3}}{2}\)
\(\Leftrightarrow sin\left(x+20^o\right)=sin60^o\)
\(\Leftrightarrow\left[{}\begin{matrix}x+20^o=60^o+k.360^o\\x+20^o=120^o+k.360^o\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=40^o+k.360^o\\x=100^o+k.360^o\end{matrix}\right.\)
2.
a, \(cos2x=-\dfrac{1}{2}\)
\(\Leftrightarrow cos2x=cos\left(\dfrac{2\pi}{3}\right)\)
\(\Leftrightarrow2x=\pm\dfrac{2\pi}{3}+k2\pi\)
\(\Leftrightarrow x=\pm\dfrac{\pi}{3}+k\pi\)
2.
b, \(cos\left(\dfrac{\pi}{6}-x\right)=\dfrac{\sqrt{3}}{2}\)
\(\Leftrightarrow cos\left(\dfrac{\pi}{6}-x\right)=cos\dfrac{\pi}{6}\)
\(\Leftrightarrow\dfrac{\pi}{6}-x=\pm\dfrac{\pi}{6}+k2\pi\)
\(\Leftrightarrow\left[{}\begin{matrix}x=k2\pi\\x=\dfrac{\pi}{3}+k2\pi\end{matrix}\right.\)
2.
e, \(cos\left(x-2\right)=-\dfrac{2}{5}\)
\(\Leftrightarrow x-2=\pm arccos\left(-\dfrac{2}{5}\right)+k2\pi\)
\(\Leftrightarrow x=2\pm arccos\left(-\dfrac{2}{5}\right)+k2\pi\)
2.
c, \(cos\left(x-\dfrac{\pi}{4}\right)=cos\dfrac{\pi}{5}\)
\(\Leftrightarrow x-\dfrac{\pi}{4}=\pm\dfrac{\pi}{5}+k2\pi\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{9\pi}{20}+k2\pi\\x=\dfrac{\pi}{20}+k2\pi\end{matrix}\right.\)