# How do you evaluate cot^-1(1) without a calculator?

${\cot}^{-} 1 \left(1\right) = \frac{\pi}{4}$.
Recall the Defn. of ${\cot}^{-} 1$ fun. :
${\cot}^{-} 1 x = \theta , x \in \mathbb{R} \iff \cot \theta = x , \theta \in \left(0 , \pi\right)$.
Since cot(pi/4)=1, &, pi/4 in (0, pi), we have, ${\cot}^{-} 1 \left(1\right) = \frac{\pi}{4}$.