Calculus III Finding length of one arc of cycloid

Question

Find the length of one arch of the cycloid

x = r(θ − sin(θ)), y = r(1 − cos(θ))

Answer 1

A Theorem states (it should proved in your text book)

If C is a cycloid defined by the parametric equations

x = a(θ - sin θ)

y = a(1 - cos θ),

then the length of one arc is 8a.

In the problem you present, the length of one arc is 8r.