Find the exact values of the other 5 trig functions if cos θ = -1/3, pi/2 < θ < pi

Question

Find the exact values of the other 5 trig functions if cos θ = -1/3, pi/2 < θ < pi

Answer 1

sin(θ) = √(1 - cos²(θ)) = √(1 - (-1/3)²) = √(8/9) = 2√2 / 3

tan(θ) = sin(θ)/cos(θ) = (2√2 / 3) / (-1/3) = -2√2

cot(θ) = 1/tan(θ) = -1 / (2√2) = -√2 / 4

scs(θ) = 1/sin(θ) = 3 / (2√2) = 3√2 / 4

sec(θ) = 1/cos(θ) = -3