Question

If cos(θ) = -8/17 and sin(θ) is negative, then sin(θ) = and tan(θ) = .

Answer 1

sin(θ) = -15/17

tan(θ) = 15/8

Explanation:

it is known that cos²(θ) + sin²(θ) = 1

cos(θ) = -8/17

cos²(θ) = 64/289

sin²(θ) = (289-64)/289

sin²(θ) = 225/289

sin(θ) = ±15/17

since sin(θ) is negative, sin(θ) = -15/17

we also know that tan(θ) = sin(θ)/cos(θ)

tan(θ) = (-15/17)/(-8/17) = (-15/17 * 17) / -8 = 15/8