Question

How do you find the value of `cot theta` given `csc theta=-2` and in quadrant IV?

Answer 1

`- sqrt3`

Explanation:

`csc t = - 2` --> `sin t = 1/(csc t) = - 1/2`.
Find cos t.
`cos ^2 t = 1 - sin^2 t = 1 - 1/4 = 3/4`
`cos t = +- sqrt3/2`
On the unit circle, if t is in quadrant IV, cos t is positive
`cot t = cos/(sin) = (sqrt3/2)(- 2/1) = - sqrt3`