1. The problem statement, all variables and given/known data A circle of C of radius b rolls on the inside of a larger circle of radius a centered at the origin. Let P be a fixed point on the smaller circle, with initial position at the point (a, 0). 2. Relevant equations x = (a-b)cos(θ)- bcos(((a-b)/b)θ) y = (a-b)sin(θ)- bsin(((a-b)/b)θ) 3. The attempt at a solution I understand part of it. Exactly what I don't understand is how thata of the big circle is related to phi of the smaller circle. Some other explanations say the arclength of the smaller circle is b(θ+Φ) when I think it should be just bΦ. Why add theta to phi all of sudden? Shouldn't the distance the smaller circle travel be bΦ and not b(θ+Φ)?