# How do you solve 5 sin^2 (alpha) - 11 sin (alpha) + 2=0?

Aug 10, 2016

$\alpha = {11.54}^{\circ}$

#### Explanation:

Let $\sin \left(\alpha\right) = x$
Hence we can write
$5 {x}^{2} - 11 x + 2 = 0$
or
$5 {x}^{2} - 10 x - x + 2 = 0$
or
$5 x \left(x - 2\right) - 1 \left(x - 2\right) = 0$
or
$\left(x - 2\right) \left(5 x - 1\right) = 0$
or
$x - 2 = 0$
or
$x = 2$
or
$5 x - 1 = 0$
or
$5 x = 1$
or
$x = \frac{1}{5}$
or
Out of the above two solutions $\sin \alpha = 2$ which is invalid
Hence
$\sin \alpha = \frac{1}{5}$
or
$\alpha = {\sin}^{-} 1 \left(\frac{1}{5}\right)$
or
$\alpha = {11.54}^{\circ}$