Rolling Around

Calculus Level pending

A unit circle rolls around the circumference of a large circle of radius 4, as shown in the figure above. The epicycloid traced by a point on the circumference of the smaller circle is given by

\(x= 5\cos t- \cos 5t\) and \(y= 5 \sin t-\sin 5t\).

Find the distance traveled by the point in one complete trip about the larger circle.

Problem from Calculus by Ron Larson.

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