# What is the equation of the tangent line of r=tan^2(theta) - sin(theta-pi) at theta=pi/4?

May 10, 2018

$r = \frac{2 + \sqrt{2}}{2}$

#### Explanation:

$r = {\tan}^{2} \theta - \sin \left(\theta - \pi\right)$ at $\frac{\pi}{4}$

$r = {\tan}^{2} \left(\frac{\pi}{4}\right) - \sin \left(\frac{\pi}{4} - \pi\right)$

$r = {1}^{2} - \sin \left(\frac{- 3 \pi}{4}\right)$

$r = 1 - \sin \left(\frac{5 \pi}{4}\right)$

$r = 1 - \left(- \frac{\sqrt{2}}{2}\right)$

$r = 1 + \frac{\sqrt{2}}{2}$

$r = \frac{2 + \sqrt{2}}{2}$