# How do you find the solution to csc^2theta-6csctheta+8=0 if 0<=theta<2pi?

##### 1 Answer
Dec 19, 2016

$\theta = \frac{\pi}{6} \mathmr{and} \theta = 5 \frac{\pi}{6} \mathmr{and} \theta = \arcsin \left(\frac{1}{4}\right) \mathmr{and} \theta = \pi - \arcsin \left(\frac{1}{4}\right)$

#### Explanation:

You can use the quadratic formula, in the form:

$x = - \frac{b}{2} \pm \sqrt{{\left(\frac{b}{2}\right)}^{2} - c}$,

useful when b is even and $a = 1$.

Then

$\csc \theta = 3 \pm \sqrt{9 - 8}$

$\csc \theta = 2 \mathmr{and} \csc \theta = 4$

that's

$\sin \theta = \frac{1}{2} \mathmr{and} \sin \theta = \frac{1}{4}$

$\theta = \frac{\pi}{6} \mathmr{and} \theta = \frac{5 \pi}{6} \mathmr{and} \theta = \arcsin \left(\frac{1}{4}\right) \mathmr{and} \theta = \pi - \arcsin \left(\frac{1}{4}\right)$