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: 68


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

Work Step by Step

We have $$z=x^2+y^2 \Longrightarrow \rho\cos\phi =\rho^2\sin^2\phi\cos^2\theta+\rho^2\sin^2\phi\sin^2\theta\\ =\rho^2\sin^2\phi .$$ That is $$\rho=\cot\phi \csc\phi .$$
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.