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 578: 56


Polar equation: $r \cos \theta-r \sin \theta=3$ $r=\dfrac{3}{ \cos \theta- \sin \theta}$

Work Step by Step

Conversion of polar coordinates and Cartesian coordinates are as follows: a) $r^2=x^2+y^2 \implies r=\sqrt {x^2+y^2}$ b) $\tan \theta =\dfrac{y}{x} \implies \theta =\tan^{-1} (\dfrac{y}{x})$ c) $x=r \cos \theta$ d) $y=r \sin \theta$ Since, we have $x=r \cos \theta$ and $y=r \sin \theta$ Thus, we have an equivalent polar equation $r \cos \theta-r \sin \theta=3$
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