Question

What is Cot(cos^-1(-39/89))?

Answer 1

`cot(cos^-1(-39/89)) = -39/80`

Explanation:

Let `theta = cos^(-1)(-39/89)`

Then `cos(theta) = -39/89`

and `theta` is in Q2, so `sin(theta) >= 0` and

`sin(theta) = sqrt(1-cos^2(theta)) = sqrt(1-39^2/89^2) = sqrt((89^2-39^2)/89^2) = sqrt((7921-1521)/89^2) = sqrt(6400/89^2) = sqrt(80^2/89^2) = 80/89`

So:

`cot(theta) = cos(theta)/sin(theta) = (-39/89)/(80/89) = -39/80`