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

Jan 23, 2017

Use the identity $\sec \left(\theta\right) = \pm \sqrt{1 + {\tan}^{2} \left(\theta\right)}$

#### Explanation:

Given: $\tan \left(\theta\right) = 4$

Substitute ${\left(4\right)}^{2}$ for ${\tan}^{2} \left(\theta\right)$ into the identity:

sec(theta) = +-sqrt(1 + 4^2

$\sec \left(\theta\right) = \pm \sqrt{17}$

Whether the secant is positive or negative cannot be determined with the given information.