\(sin\left(\dfrac{x+\pi}{5}\right)=-\dfrac{1}{2}\)
\(\Rightarrow\left[{}\begin{matrix}\dfrac{x+\pi}{5}=-\dfrac{\pi}{6}+k2\pi\\\dfrac{x+\pi}{5}=\dfrac{7\pi}{6}+k2\pi\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-\dfrac{11\pi}{6}+k10\pi\\x=\dfrac{29\pi}{6}+k10\pi\end{matrix}\right.\)
4.
\(2sin\left(2x-10^0\right)=\sqrt{3}\Rightarrow sin\left(2x-10^0\right)=\dfrac{\sqrt{3}}{2}\)
\(\Rightarrow\left[{}\begin{matrix}2x-10^0=60^0+k360^0\\2x-10^0=120^0+k360^0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=35^0+k180^0\\x=65^0+k180^0\end{matrix}\right.\)
\(\Rightarrow x=\left\{-145^0;35^0;-115^0;65^0\right\}\) có 4 nghiệm
C3
\(sin\left(\dfrac{x+\Pi}{5}\right)=sin\left(\dfrac{-\pi}{6}\right)\)
<=>\(^{\left[{}\begin{matrix}\dfrac{x+pi}{5}=\dfrac{-pi}{6}+k2pi\\\dfrac{x+pi}{5}=\dfrac{7pi}{6}+k2pi\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\dfrac{x}{5}=-\dfrac{11pi}{30}+k2pi\\\dfrac{x}{5}=\dfrac{29pi}{30}+k2pi\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{11pi}{6}+\dfrac{k2pi}{5}\\x=\dfrac{29pi}{6}+\dfrac{k2pi}{5}\end{matrix}\right.\)
