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: 60

Answer

Please see the figure attached.

Work Step by Step

In spherical coordinates, $\theta$ is the polar angle of the projection $Q$ of a point $P$ onto the $xy$-plane. Since it is constant $\theta = \frac{\pi }{2}$, it is located in the $yz$-plane. While $\phi$ is the angle of declination, which measures how much the ray through a point $P$ declines from the vertical. Since it is constant $\phi = \frac{\pi }{4}$, this is a line in the $yz$-plane. Since $\rho \ge 1$, the line starts from $\rho=1$.
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