# How do you find the exact value for tan^-1(tan (7pi/4))?

Feb 15, 2016

$k \pi + 3 \frac{\pi}{4} , k \in \mathbb{Z}$

#### Explanation:

${\tan}^{-} 1 \left(\tan \left(7 \frac{\pi}{4}\right)\right)$

By the trigonometric circle you can see that $\tan \left(7 \frac{\pi}{4}\right) = \tan \left(- \frac{\pi}{4}\right) = - 1$

So the expression simplifies in:

${\tan}^{-} 1 \left(- 1\right)$

So which are the angles which tangent is -1?

Again by the trigonometric circle you can see that:

${\tan}^{-} 1 \left(- 1\right) = k \pi + 3 \frac{\pi}{4} , k \in \mathbb{Z}$