# Solve the equation on the interval [0,2pi] sin 4x=(sqrt(3))/(2)

Solve the equation on the interval $\left[0,2\pi \right]$
$\mathrm{sin}4x=\frac{\sqrt{3}}{2}$
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Lillianna Mendoza
$\mathrm{sin}4x=\frac{\sqrt{3}}{2}$
let $\varphi =4x$
$\mathrm{sin}\varphi =\frac{\sqrt{3}}{2}$
$\varphi =\frac{\pi }{3},\frac{2\pi }{3}$
$\varphi =4x=\frac{\pi }{3},\frac{2\pi }{3}$
$\therefore x=\frac{\pi }{12},\frac{\pi }{6}$

termegolz6
$x=\frac{\pi }{12},\frac{11\pi }{12}$ , 15 or 165 degree
times $4=\frac{\pi }{3},\frac{2\pi }{3}$ 30 or 150 degree
$\mathrm{sin}\left(30\right)and\mathrm{sin}\left(150\right)=\frac{\sqrt{3}}{2}$
Therefore $x=\frac{\pi }{12},\frac{11\pi }{12}$