Question

Given `tantheta=-5/12` and `(3pi)/2<theta<2pi`, how do you find `tan(theta/2)`?

Answer 1

You use the formula of the tangent of the double angle and you solve the resulting equation choosing the right solution based on the interval specified

Explanation:

`tan(theta) = (2tan(theta/2))/(1-tan^2(theta/2)`

or

`-5/12 = (2tan(theta/2))/(1-tan^2(theta/2)`

Pose `t = tan(theta/2)`

You have:

`5t^2-24t-5=0`

`t=(12+-sqrt(144+25))/5`

If `(3pi)/2 < theta < 2pi` then `(3pi)/4 < theta/2 < pi`, and the tangent is negative in this interval, so:

`tan(theta/2) = (12 -sqrt(169))/5 = -1/5`