given that tan θ= -8/15 and θ is in quadrants 2, find: sin2 θ, cos2 θ, and tan2 θ

Answer 1

8² + 15² = 17²

Thus, in quadrant 2, if tan θ = -8/15 and θ is in quadrant 2, (cos θ , sinθ ) is (-15/17, 8/17)

sin 2 θ = 2 sin θ cos θ = 2 * 8/17 * -15/17 = -240/ 289

cos 2 θ = cos² θ - sin² θ = 225/289 - 64/289 = 159/289

We can calculate tan 2 θ in 2 ways: sin 2 θ / cos 2 θ = -240/ 289/(159/289) = -240/159

tan 2 θ = 2 tan θ / 1- tan² θ = 2 * -8/15/1 - (-8/15)² = -16/15/((159/225) = -16 * 15/159 = -240/159