Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 13 - Vector Geometry - 13.7 Cylindrical and Spherical Coordinates - Preliminary Questions - Page 699: 4


$\phi_0=0 $, $\phi_0=\pi $

Work Step by Step

In spherical coordinates, we have $$ \begin{aligned} &x=\rho \sin \phi \cos \theta\\ &y=\rho \sin \phi \sin \theta\\ &z=\rho \cos \phi \end{aligned} $$ When $\phi_0=0 $, we get $x=0,y=0, z=\rho$, which is a half-line. When $\phi_0=\pi $, we get $x=0,y=0, z=-\rho$, which is a half-line.
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