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 - Exercises - Page 700: 33



Work Step by Step

Since $\rho=3, \, \theta=0 \, \phi=\frac{\pi}{2}$ and $$ x=\rho\cos \theta\sin \phi,\quad y=\rho\sin\theta\sin\phi, \quad z=\rho\cos \phi,$$ then we have $$ x=3\cos 0\sin \frac{\pi}{2}=3, $$ $$ y=3\sin 0\sin \frac{\pi}{2}=0, $$ $$ z=3\cos \frac{\pi}{2}=0.$$ Hence, the rectangular coordinates are $(3,0,0)$.
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