Question

How do you find sin 2θ, given cos θ = 5/13 and θ lies in Quadrant IV?

Answer 1

Use the identity sin2θ = 2sinθcosθ.

You know cosθ so you have to use the Pythagorean identity to find sinθ = -12/13.

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