# How do you use csctheta=4 to find sectheta?

##### 1 Answer
Feb 4, 2017

$\sec \theta = \pm \frac{4}{\sqrt{15}}$

#### Explanation:

As $\csc \theta = 4$, $\sin \theta = \frac{1}{\csc} \theta = \frac{1}{4}$

and $\cos \theta = \sqrt{1 - {\sin}^{2} \theta} = \sqrt{1 - {\left(\frac{1}{4}\right)}^{2}} = \sqrt{\frac{15}{16}} = \pm \frac{\sqrt{15}}{4}$

and $\sec \theta = \pm \frac{4}{\sqrt{15}}$