Find sin 2(theta). cos(theta) = 24/25, theta lies in quadrant IV

Think: 7-24-25 right triangle

cos θ = 24/24, so sin θ = -7/25.

sin 2θ = 2 sin θ cos θ = 2 (-7/25) (24/25) = -336/625

cos(θ) = 24/25

sin(2θ) = 2*sin(θ)*cos(θ) = 2(24/25)(-√(1 - 24²/25²)) = (48/25)(-7/25) = -336/625