Answer
The solutions of the equation are $x=\frac{\pi }{6}+2n\pi $ or $x=\frac{11\pi }{6}+2n\pi $, where n is any integer.
Work Step by Step
The x in $\cos x=\frac{\sqrt{3}}{2}$. Because $\cos \frac{\pi }{6}=\frac{\sqrt{3}}{2}$, so, the solutions of $\cos x=\frac{\sqrt{3}}{2}$ in [0,2 $\pi $ ) are:
$x=\frac{\pi }{6}$
$\begin{align}
& x=2\pi -\frac{\pi }{6} \\
& =\frac{12\pi }{6}-\frac{\pi }{6} \\
& =\frac{11\pi }{6}
\end{align}$
The period of the sine function is $2\pi $, and the solutions are given by:
$x=\frac{\pi }{6}+2n\pi $ or $x=\frac{11\pi }{6}+2n\pi $, where n is any integer.
