If tan (x) =-4/3 and x is in Q2....then y is positive, x is negative and r = sqrt ( 3^2 + 4^2) = sqrt (25) = 5
sin x = 4/5 cos x = -3/5
sin (2x) =2 sin (x) cos (x) = 2 ( 4/5) (-3/5) = -24/25
cos (2x) = cos^2(x) - sin^2(x) = (-3/5)^2 - (4/5)^2 = 9/25 - 16/25 = -7/25
tan (2x) = sin(2x) / cos (2x) = (-24/25) / ( -7/25) = -24/-7 = 24/7