If x = 6sin(theta), use trigonometric substatution to write the square root of 36-x^2 as a trigonometric function of theta, where 0 is less then theta wich is less then pi/2

Answer 1

x = 6sin(θ)

f(x) = 36 - x^2

Substituting x = 6Sin(θ) yields:

f(x) = 36 -36Sin^2(θ) = 36( 1 - Sin^2(θ) ) = 36Cos^2(θ) because Sin^2(θ) + Cos^2(θ) = 1