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: 35

Answer

The rectangular coordinates are $(0,0,3)$.

Work Step by Step

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