Trig Use the given information about θ to find the exact values of the following?

When π < θ < 3π/2, sin(θ) < 0 and cos(θ) < 0
Thus, when π/2 < θ/2 < 3π/4, sin(θ/2) > 0 and cos(θ/2) < 0

Given tan(θ) = 12/5

sin(θ) = -12/√(12² + 5²)
sin(θ) = -12/13

cos(θ) = -5/√(12² + 5²)
cos(θ) = -5/13

sin(2θ) = 2 sin(θ) cos(θ)
sin(2θ) = 2 × (-12/13) × (-5/13)
sin(2θ) = 120/169

sin²(θ/2) = [1 - cos(θ)]/2
sin²(θ/2) = [1 -(-5/13)]/2
sin²(θ/2) = 9/13
sin(θ/2) = 3/√13
sin(θ/2) = (3√13)/13

cos(2θ) = cos²(θ) - sin²(θ)
cos(2θ) = (-5/13)² - (-12/13)²
cos(2θ) = -119/169

cos²(θ/2) = [1 + cos(θ)]/2
cos²(θ/2) = [1 + (-5/13)]/2
cos²(θ/2) = 4/13
cos(θ/2) = -2/√13
cos(θ/2) = -(2√13)/13

tan(2θ) = 2 tan(θ) / [1 - tan²(θ)]
tan(2θ) = 2 (12/5) / [1 - (12/5)²]
tan(2θ) = (24/5) / (-119/25)
tan(2θ) = (24/5) × (-25/119)
tan(2θ) = -120/119

tan(θ/2) = sin(θ/2) / cos(θ/2)
tan(θ/2) = (3/√13) / (-2/√13)
tan(θ/2) = -3/2

sin 2θ = 2sinθcosθ =
2*60/169 = 120/169

Hint:
sin(t)=-12/13
cos(t)=-5/13