Question

How do you find the exact value of `cot(arcsin ((-7/13))`?

Answer 1

`+-2sqrt(30)/7`

Explanation:

it depends on how you define range of `arcsin(theta)`
1. range of `arcsin(theta) = {y|0 < y <= pi/2 , pi < y <=3/2*pi}`
The angle of `arcsin(-7/13)` is at third quadrant.
`cot(arcsin(-7/13))=-sqrt(13^2-(-7)^2)/(-7)=2sqrt(30)/7`
2. range of `arcsin(theta) = {y|-pi/2 <= y <0, 0 < y <= pi/2}`
The angle of `arcsin(-7/13)` is at fourth quadrant.
`cot(arcsin(-7/13))=sqrt(13^2-(-7)^2)/(-7)=-2sqrt(30)/7`