?If a circle \(C\) with radius 1 rolls along the outside of the circle

Chapter 14, Problem 24

(choose chapter or problem)

If a circle  \(C\)  with radius 1 rolls along the outside of the circle \(x^{2}+y^{2}=16\), a fixed point  \(P\)  on  \(C\)  traces out a curve called an epicycloid, with parametric equations \(x=5 \cos t-\cos 5 t, y=5 \sin t-\sin 5 t\). Graph the epi- cycloid and use (5) to find the area it encloses.

Equation Transcription:

Text Transcription:

x^2 + y^2 = 16

C

P

C

x = 5 cos t - cos 5t, y = 5 sin t - sin 5t