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 603: 20


The answer is $\pi \leq t<2 \pi$.

Work Step by Step

The circle is traversed once in the counterclockwise direction as $t$ varies over an interval $[0,2 \pi )$. At $t=\pi$, we have $ c(\pi)=(-1,0)$, so the lower half of the circle starts from $\pi$. Hence, for $\pi \leq t<2 \pi$, the equation $c(t)=(\cos t, \sin t)$ traces the lower half of the unit circle.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.