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: 15

Answer

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Work Step by Step

Conversion formulas: $\left\{\begin{array}{ll} (x,y)=(r\cos\theta,r\sin\theta) & \\ r^{2}=x^{2}+y^{2}, & \tan\theta=\frac{y}{x} \end{array}\right.$ The angle is any angle between $0$ and $\pi/6$ (1st quadrant) and the directed distance r is positive, so only points in the 1st quadrant are involved. $\theta=0$ is the +x axis ray, $\theta=\pi/6$ is the ray on the line $y=(\displaystyle \tan\frac{\pi}{6})x$, from the origin into the 1st quadrant.
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