Question

How do you find the exact value of `cot(arcsin(-12/13))`?

Answer 1

`cot(arcsin(-12/13))=color(green)(-5/12)`

Explanation:

Remember that the `arcsin` function is defined as having a range `(-pi/2,+pi/2]`

The `arcsin(-12/13)` can be represented by a triangle in the standard position with opposite side (i.e. `y` coordinate): `(-12)`
and hypotenuse `(13)`

Based on the Pythagorean Theorem, this triangle would have an adjacent side with the length `sqrt(13^2-(-12)^2) =5`

Since `cot="adjacent"/"opposite"`

`cot(arcsin(-12/13))=5/(-12)=-5/12`