Question

How do you solve and find the value of `cot(sin^-1(7/9))`?

Answer 1

`+- (4sqrt2)/7`

Explanation:

`sin x = 7/9`
cot (arcsin x) = cot x
Use trig identity:
`1 + cot^2 x = 1/(sin^2 x) = 81/49`
`cot^2 x = 81/49 - 1 = 32/49`
`cot x = +- (4sqrt2)/7`.
`sin x = 7/9` --> x could be in Quadrant 1 or Quadrant 2. There fore,
cot x could be either negative or positive.