Wish I could help more but I skipped trig and went to AP calc...so I'm not sure how much weight you should put into my verifying of your answers.
assuming the form Asin(wx+c) -d ...
Looks right to me.... amplitude = 2, yep. period 2pi/w. 2pi/(4/3) = 3pi/2, vertical translation, yeah. phase change, (2pi/3/(4/3)=pi/2... so looks good to me, just simplify fractions.