# How do you find the exact value of tan^-1(tan(-(3pi)/4))?

$\frac{\pi}{4}$
First of all, observe that $\tan \left(- \frac{3 \pi}{4}\right) = \tan \left(\frac{\pi}{4}\right)$, since the two angles are $\pi$ radians apart.
Then, ${\tan}^{- 1}$ is the inverse function of the tangent, which means exactly that ${\tan}^{- 1} \left(\tan \left(x\right)\right) = x$, if $x$ is an angle between $- \frac{\pi}{2}$ and $\frac{\pi}{2}$, since this is the specified range for the inverse tangent function.