Question

How do I find the value of `cot(-240^o)`?

Answer 1

`cot(-240^o) = sqrt(3)/3`

Explanation:

`-240^o` is equivalent to `120^o`

A `120^o` is in Quadrant II with a reference angle of `60^o`

`60^o` is a standard angle with `tan(60^o) = sqrt(3)`
`color(white)("XXXX")` `color(white)("XXXX")` `color(white)("XXXX")` `rarr cot(60^o) = 1/sqrt(3) = sqrt(3)/3`

In Quadrant II, `tan` (and, therefore, `cot`) is negative,

so
`color(white)("XXXX")` `cot(-240^o) = -sqrt(3)/3`