Question

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

Answer 1

`pi/4`

Explanation:

First of all, observe that `tan(-(3pi)/4) = tan(pi/4)`, since the two angles are `pi` radians apart.

Then, `tan^{-1}` is the inverse function of the tangent, which means exactly that `tan^{-1}(tan(x)) = x`, if `x` is an angle between `-pi/2` and `pi/2`, since this is the specified range for the inverse tangent function.