Question

How do you calculate `(tan^-1 (1))`?

Answer 1

If a = tan^(-1)1, a has just one value `pi/4 in [0, pi]`. There are two values `pi/4 and (5pi)/4 in [0. 2pi]` and `npi+pi/4, n=0, +-1, +-2, .. in (-oo, +oo)`..

Explanation:

If a = tan^(-1)1 and if the range for a is not specified,

`a = npi+pi/4, n=0, +-1, +-2, .. in (-oo, +oo)`.

n=0 gives `pi/4 in [0. pi]`

n=0, 1 give `a=pi/4, (5pi)/4 in [0, 2pi]`..