Thought I did this one but it was just very similar. Again there's a q and a theta I'm just going to assume are the same.
[tex] \sin \theta = \pm \sqrt{1 - \cos^2 \theta}[/tex]
[tex] \sin \theta = + \sqrt{1 - (3/5)^2} = \frac 4 5[/tex]
I picked positive because we're in the first quadrant.
[tex] \sin 2 \theta = 2 \sin \theta \cos \theta[/tex]
[tex]\sin 2 \theta = 2 (\frac 4 5)(\frac 3 5) = \frac {24}{25}[/tex]
