University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 10 - Section 10.3 - Polar Coordinates - Exercises - Page 577: 12

Answer

$x^{2}+y^{2}\leq 4$ .

Work Step by Step

$\left\{\begin{array}{ll} (x,y)=(r\cos\theta,r\sin\theta) & \\ r^{2}=x^{2}+y^{2}, & \tan\theta=\frac{y}{x} \end{array}\right.$ $r$ is the directed distance of the point from the pole. $r=2$ defines all points at a distance of 2 units from the pole. $0\leq r\leq 2$ describes all points on or inside the circle of radius 2. In Cartesian coordinates, $x^{2}+y^{2}\leq 4$
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