Question

How do you use `csctheta=4` to find `tantheta`?

Answer 1

`tan t = +- sqrt17/4`

Explanation:

`csc t = 1/sin t = 4`
`sin t = 1/4`
t could be either in Quadrant 1 or Quadrant 2.
`cot^2 t = 1/(1 + sin^2 t) = 1/(1 + 1/16) = 16/17`
`cot t = +- 4/sqrt17`.
`tan t = 1/(cot t) = +- sqrt17/4`
If t lies in Quadrant 1 --> tan t is positive
If t lies in Quadrant 2 --> tan t is negative.