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: 38

Answer

$(-0.385,-0.24,-0.208)$.

Work Step by Step

Since $\rho=0.5, \, \theta=3.7, \, \phi=2$ and $$ x=\rho\cos \theta\sin \phi,\quad y=\rho\sin\theta\sin\phi, \quad z=\rho\cos \phi,$$ then we have $$ x=0.5\cos3.7\sin 2=-0.385, $$ $$ y=0.5\sin 3.7\sin 2=-0.24, $$ $$ z=0.5\cos 2=-0.208.$$ Hence, the rectangular coordinates are $(-0.385,-0.24,-0.208)$.
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