Seems to be a q and a theta here; presumably they're the same.
[tex] \sin \theta = - \frac 3 5 [/tex]
[tex] \cos \theta = + \sqrt{ 1- \sin^2 \theta} = \sqrt{1- 9/25} = \frac 4 5 [/tex]
I chose the positive cosine because we're (almost) told [tex]\theta[/tex] is in the fourth quadrant.
[tex] \tan \theta = \dfrac{\sin \theta}{\cos \theta } = \dfrac{-3/5}{4/5} = - \frac 3 4[/tex]
[tex] \tan 2 \theta = \dfrac{2 \tan \theta}{1 - \tan^2 \theta} = \dfrac{-3/2}{1 - 9/16} = - \dfrac{24}{7}[/tex]
Choice b
