# Find all real numbers in the interval [0, 2pi) round to the nearest tenth? 3 sin^2x=sin x

Apr 17, 2018

$x = {0}^{c} , {0.34}^{c} , {\pi}^{c} , {2.80}^{c}$

#### Explanation:

Rearrange to get:
$3 {\sin}^{2} x - \sin x = 0$

$\sin x = \frac{1 \pm \sqrt{{1}^{2}}}{6}$

$\sin x = \frac{1 + 1}{6} \mathmr{and} \frac{1 - 1}{6}$

$\sin x = \frac{2}{6} \mathmr{and} \frac{0}{6}$

$\sin x = \frac{1}{3} \mathmr{and} 0$

$x = {\sin}^{-} 1 \left(0\right) = 0 , \pi - 0 = {0}^{c} , {\pi}^{c}$
or
$x = {\sin}^{-} 1 \left(\frac{1}{3}\right) = 0.34 , \pi - 0.34 = {0.34}^{c} , {2.80}^{c}$

$x = {0}^{c} , {0.34}^{c} , {\pi}^{c} , {2.80}^{c}$