Question

How do you evaluate `tan^-1(-1/sqrt3)` without a calculator?

Answer 1

`tan^-1(-1/sqrt3) = -pi/6`

Explanation:

Let `tan^-1(-1/sqrt3) = theta`, then `tan theta = -1/sqrt3; tan(-pi/6)=-1/sqrt3 :. theta = -pi/6 or tan^-1(-1/sqrt3) = -pi/6`
The range of `tan^-1 theta` is `(-pi/2 , pi/2) and -pi/6 in (-pi/2 , pi/2)`[Ans]