Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 10 - Analytic Geometry - Chapter Review - Cumulative Review - Page 701: 9

Answer

$r=8\sin\theta$ (see graph)

Work Step by Step

We are given the circle: Center: $(0,4)$ Radius: $4$ The rectangular equation of the circle is: $(x-0)^2+(y-4)^2=4^2$ $x^2+(y-4)^2=16$ Write the equation in polar form using the formulas: $x=r\cos\theta$ $y=r\sin\theta$ $x^2+y^2=r^2$ $(r\cos\theta)^2+(r\sin\theta-4)^2=16$ $r^2\cos^2\theta+r^2\sin^2\theta-8r\sin\theta+16=16$ $r^2(\cos^2\theta+\sin^2\theta)-8r\sin\theta=0$ $r^2-8r\sin\theta=0$ $r(r-8\sin\theta)=0$ $r-8\sin\theta=0$ $r=8\sin\theta$
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