Question

Given `tantheta=-3/4` and `pi/2<theta<pi`, how do you find `tan(theta/2)`?

Answer 1

The answer is `=tan(theta/2)=3`

Explanation:

You can use the formula `tan2theta=(2tantheta)/(1-tan^2theta)`

`:. tantheta=(2tan(theta/2))/(1-tan^2(theta/2))`
Let `tan(theta/2)=t`
then `-3/4=(2t)/(1-t^2)`
`-3+3t^2=8t`
`3t^2-8t-3=0`
This is a quadratic equation
`Delta=64+36=100`
So, `t=(8+-sqrt100)/6=8+-10`

`t=3` or `t=-1/3`

We keep only `t=3` as `pi/2< theta < pi`