Calculus (3rd Edition)

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

Chapter 13 - Vector Geometry - 13.7 Cylindrical and Spherical Coordinates - Exercises - Page 700: 31

Answer

$$r=\pm2$$

Work Step by Step

Since $$ x=r\cos \theta,\quad y=r\cos \theta, \quad z=z,$$ then $ x^2+y^2=4$ takes the form $$ r^2\cos^2\theta+r^2\sin^2\theta =4 \\ r^2=\frac{4}{\cos^2\theta+\sin^2\theta}=4 \\ r=\pm2$$
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