if cos theta = 12/13 and 3pi/2 to 2pi:

Question

evaluate sin (2theta)

Answer 1

cosθ = 12/13 and  3π/2 ≤ θ ≤ 2π

 

Since θ lies in Quadrant 4, sinθ < 0

 

(cosθ)² + (sinθ)² = 1, so sinθ = -√(1 - cos²θ) = -5/13

 

sin2θ = 2sinθcosθ = 2(12/13)(-5/13) = -120/169