Anonymous

cosθ = 1/z sin²θ = 1-cos²θ = (z²-1)/z² sinθ = ±√(z²-1)/z cotθ = cosθ/sinθ = ±1/√(z²-1) = ±√(z²-1)/(z²-1)

Anonymous

Let y= cos^-1(1/z) cos(y) = 1/z cos = adj/hyp adj=1 hyp = z opp = sqrt(z^2-1) (Pythogorean Theorem) cot (cos^-1(1/z)) = cot(y) cot = adj/opp = 1/sqrt(z^2-1)