## Calculus (3rd Edition)

Published by W. H. Freeman

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

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