Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.1 Parametric Equations - Exercises - Page 605: 78

Answer

The path of the curve will be at some $t$ higher and at some $t$ lower than the generating circle.

Work Step by Step

From Exercise 77 we obtain the parametric equation of the cycloid: $c(t)=(R{\ }t-h \sin t,R-h \cos t)$. In the case $h>R$, the path of the curve will be at some $t$ higher and at some $t$ lower than the generating circle. Since the lowest point of the circle is at $y=0$, the curve will at some point goes below the $x$-axis. This is illustrated in the figure attached.
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