I'm unsure about this double angle problem

Question

How should I do this problem: find the value of sin 2(theta) if theta is in the 4th quadrant and sin(theta) equals -1/2. I feel like this problem isn't that difficult, but I'm unsure if I did it right

 

 

Answer 1

sin(2θ) = 2sinθcosθ

 

In Quadrant 4, sinθ < 0 and cosθ > 0

 

sinθ = -1/2, cosθ = √(1 - sin²θ) = √3/2

 

So, sin(2θ) = 2sinθcosθ = 2(-1/2)(√3/2) = -√3/2