Given sin ∅ = 15/17 where 90o < ∅ < 180o, find sin 2∅.

Answer 1

Since the angle lies in quadrant 2, cosine is negative.

cosθ = -√[1 - sin²θ] = -√[1 - 225/289] = -8/17

So, sin(2θ) = 2sinθcosθ = 2(15/17)(-8/17) = -240/289