Find exact value of sin 2θ, cos 2θ, and tan 2θ.

If tan θ = 3/4, pi < θ < 3pi/2, find exact value of sin 2θ, cos 2θ, and tan 2θ.

show steps plz

tan(t) = 3/4

sin(t) / cos(t) = 3/4
4sin(t) = 3cos(t)
16sin(t)^2 = 9cos(t)^2
16sin(t)^2 = 9 - 9sin(t)^2
25sin(t)^2 = 9
sin(t)^2 = 9/25
sin(t) = +/- 3/5

We're in Q3, so sin(t) = -3/5

cos(t)^2 + sin(t)^2 = 1
cos(t)^2 + 9/25 = 25/25
cos(t)^2 = 16/25
cos(t) = +/- 4/5

Q3, cos(t) = -4/5

sin(2t) =>
2sin(t)cos(t) =>
2 * (-3/5) * (-4/5) =>
2 * 12 / 25 =>
24/25

cos(2t) =>
cos(t)^2 - sin(t)^2 =>
16/25 - 9/25 =>
7/25

tan(2t) =>
sin(2t) / cos(2t) =>
(24/25) / (7/25) =>
24/7