Question

find exact value: inverse tan(tan 7pi/4). Medal to whoever can help describe the steps. Im not good at solving the radians.

Answer 1

\[\tan \frac{ 7\pi }{ 4 }=\tan \left( 2\pi-\frac{ \pi }{4 } \right)=-\tan \frac{ \pi }{4 }=\tan \left( \frac{ -\pi }{4 } \right)\]
\[\tan^{-1} \tan \theta=\theta \]

Answer 2

Maybe it helps to look at a drawing of y=tan x.
In the image, follow the arrows: first to x=7pi/4, then to -1 (=tan 7pi/4).
The inverse tan works only in the center part of the graph, so you have to go all the way left to -pi/4. That is the inverse tangent of -1, so that is your answer!