Find parametric equations for the hypocycloid that is produced when we track a point on a circle of radius 1/4 that rotates inside a circle of radius 1. Show that these equations are equivalent to (sin^3 t, cos^3 t).
The Attempt at a Solution
I have the intended solution except for one step. The book claims that the small circle rotates 3 times every time it rotates once inside the big circle. That makes sense because of how the points line up... But the circumference of the big circle is 4 times that of the small one, and the surfaces are always touching, so why isn't it 4 times?