Question

How do you find `cot^-1 (-1/sqrt3)` without using a calculator?

Answer 1

150, 330 degrees

Explanation:

Let the given expression be equal to y, so that cot y= `-1/sqrt3`.
`1/sqrt3` is the value of cot for 30 degrees, as can be seen from the unit circle.

Since cot would be negative in IInd and IVth quadrant, coty would be `-1/sqrt3` for y= 180-30= 150 and y= 360-30= 330 degrees