Question

How do you evaluate `cot(arcsin(-5/8)`?

Answer 1

Let `t=arcsin(-5/8)`

Then `t` is in `[- pi/2, pi/2]` and `sint = -5/8`

Find `cost` (I'm sure you have done this kind of problem by now.)

Because `-pi/2 < t < pi/2`, we know that `cost > 0`

`cost = sqrt39 / 8`

And `cot t = cost/sint =- sqrt39 / 5`

Method 2

Use `cot^2t =csc^2t -1` together with `-pi/2 < t < pi/2`, so we know that `cos t > 0` and so `cot t < 0`

`csc t = -8/5`, so `cot^2t =(-8/5)^2 -1 = 39/25` and so on