Question

How do you evaluate `cot^-1(-5)`?

Answer 1

`348.69^@` or `168.69^@`

Explanation:

`theta=cot^-1(-5)`
`cottheta=-5`
`1/tantheta=-5`
`tantheta=-1/5`
`theta=tan^-1(-1/5)`
`theta~~-11.31^@(348.69^@)`

However, according to the CAST rule, `cottheta` and `tantheta` are also negative in second quadrant.

To find the second possible angle, find the related acute angle, and subtract the value from `180^@`.

Finding the related acute angle:
`360^@-348.69^@`
`=11.31^@`

Finding the second possible angle:
`180^@-11.31^@`
`=168.69^@`

`:.`, the possible angles are approximately `348.69^@` and `168.69^@`.