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

1 Answer
Nov 7, 2016

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