Hypocycloid The graph of the parametric equations is a hypocycloid. The graph is the

Chapter 6, Problem 6.1.1.217

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Hypocycloid The graph of the parametric equations x = 2 cos t + cos 2t, y = 2 sin t - sin 2t y = 1 - cos t?  is a hypocycloid. The graph is the path of a point P on a circle of radius 1 rolling along the inside of a circle of radius 3, as illustrated in the figure.

(a) Graph simultaneously this hypocycloid and the circle of radius 3.

(b) Suppose the large circle had a radius of 4. Experiment! How do you think the equations in part (a) should be changed to obtain defining equations? What do you think the hypocycloid would look like in this case? Check your guesses.

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