abondantQ

2021-08-15

Find all solutions of the equation in the interval $\left[0,2\pi \right)$
$\mathrm{cos}2x=\frac{\sqrt{3}}{2}$

funblogC

We use Trigonometry table to find solutions of equation
$\mathrm{cos}2x=\frac{\sqrt{3}}{2}$
$\mathrm{cos}2x=\mathrm{cos}\frac{\pi }{6}$
$2\pi =\frac{\pi }{6}$
$x=\frac{\pi }{12}$
$\mathrm{cos}2x=\mathrm{cos}\left(2\pi -\frac{\pi }{6}\right)$
$\mathrm{cos}2x=\mathrm{cos}\left(\frac{11\pi }{6}\right)$
$2x=\frac{11\pi }{6}$
$x=\frac{11\pi }{12}$
Solution of equation:
$x=\frac{\pi }{12},\frac{11\pi }{12}$

Jeffrey Jordon