Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 11: Parametric Equations and Polar Coordinates - Section 11.3 - Polar Coordinates - Exercises 11.3 - Page 663: 22

Answer

See image:

Work Step by Step

The $r= -1$ indicates that this region is a part of the circle around the pole, with radius 1, and points that terminate in opposite quadrants of $\theta's$ terminal sides are represented. The angle ranges form $0$ to $\pi$, which covers the upper part of the circle, but because r is negative, we take the points diametrically opposed, that is, the lower semicircle is the graph.
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