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: 70


$$\rho=2 \cot\phi \csc\phi \csc 2\theta.$$

Work Step by Step

We have $$z=xy\Longrightarrow \rho \cos\phi=\rho^2\sin^2\phi\cos\theta\sin\theta\\ =\frac{1}{2}\rho^2\sin^2\phi \sin2\theta .$$ That is $$\rho=2 \cot\phi \csc\phi \csc 2\theta.$$
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