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

Question

A. -240/289

B. 240/289

C. -289/161

D. -289/240

Answer 1

The angle constraint puts cos(θ) in Quadrant 2, so cos(θ) will be negative

The double angle formula:

sin(2θ) = 2sin(θ)cos(θ)

We know sin(θ) = 15/17. We need to find cos(θ). This just happens to be a Pythagorean triple(8,15,17),

so cos(θ) = -8/17

sin(2θ) = 2(15/17)(-8/17) = -240/289 ≈ -0.83