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: 67

Answer

$$\rho=\tan\phi \sec\phi \cos\theta.$$

Work Step by Step

We apply the equations of this section (page 699). We have $$x=z^2 \Longrightarrow \rho\sin\phi\cos\theta=\rho^2\cos^2\phi .$$ That is $$\rho=\tan\phi \sec\phi \cos\theta.$$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.