Question

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

Answer 1

`cot^-1(1)=pi/4`.

Explanation:

Recall the Defn. of `cot^-1` fun. :

`cot^-1x=theta, x in RR iff cottheta=x, theta in (0, pi)`.

Since `cot(pi/4)=1, &, pi/4 in (0, pi),` we have, `cot^-1(1)=pi/4`.