Question

How do you evaluate `cot [sin^-1 (- sqrt2 / 3)]`?

Answer 1

`+-sqrt (7 / 2)`

Explanation:

Let `a = sin^(-1)-sqrt 2 / 3`. Then,`sin a=-sqrt 2 / 3<0`.

Accordingly, a is in the 3rd quadrant or in the 4th.

So, `cos a = +-sqrt(1-sin^2a)=+-sqrt 7 / 3`.
The answer is `cot a = cos a/sin a = +- sqrt (7/2)`.