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 662: 13

Answer

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Work Step by Step

Conversion formulas: $\left\{\begin{array}{ll} (x,y)=(r\cos\theta,r\sin\theta) & \\ r^{2}=x^{2}+y^{2}, & \tan\theta=\frac{y}{x} \end{array}\right.$ $r$ is the distance of the point from the pole. $r=1$ defines all points at a distance of 1 unit from the pole. So, $r \geq 1$ describes all points on or outside the circle of radius 1 In Cartesian coordinates, $x^{2}+y^{2} \geq 1$
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