Answer
$$\rho=\cot\phi \csc\phi .$$
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 $$\rho=\cot\phi \csc\phi .$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
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
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