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

May 18, 2016

If a = tan^(-1)1, a has just one value $\frac{\pi}{4} \in \left[0 , \pi\right]$. There are two values $\frac{\pi}{4} \mathmr{and} \frac{5 \pi}{4} \in \left[0. 2 \pi\right]$ and $n \pi + \frac{\pi}{4} , n = 0 , \pm 1 , \pm 2 , . . \in \left(- \infty , + \infty\right)$..

#### Explanation:

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

$a = n \pi + \frac{\pi}{4} , n = 0 , \pm 1 , \pm 2 , . . \in \left(- \infty , + \infty\right)$.

n=0 gives $\frac{\pi}{4} \in \left[0. \pi\right]$

n=0, 1 give $a = \frac{\pi}{4} , \frac{5 \pi}{4} \in \left[0 , 2 \pi\right]$..