Trigonoemtry Year 11 Question (T-formula) (1 Viewer)

[wiliaamnguuyen]

Hello, does anyone know how to solve this?
If tan (theta/2) = t
solve for t in the equation 12tan(theta) = 5 and 180 degrees < theta < 270 degrees.

So I solved for t in the equation by subbing in t into 12 (2t/1-t^2) = 5.

Solved it, and got two roots: t=1/5 and t=-5
How do I determine which one of those two answers is in the domain of 180<theta<270?

 

[braintic]

If θ is between 180 & 270, then θ/2 is between 90 θ 135, ie. 2nd quadrant, so tan θ/2 is negative.

 

[wiliaamnguuyen]

Oh thank you!