Question

If x = 6sinθ, use trigonometric substitution to write square root 36-x^2 as a trigonometric function of θ, where where 0<θ< pi/2

Answer 1

36-x^2
= 36-36sin^2θ
= 36(1-sin^2θ)
= 36cos^2θ

so, √(36-x^2) = 6cosθ