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: 39



Work Step by Step

Since $ x=\sqrt3, \, y=0, \, z=1$ and $$\rho=\sqrt{x^2+y^2+z^2},\quad \theta=\tan^{-1}( y/x), \quad \phi=\cos^{-1}(z/\rho),$$ then we have $$\rho=\sqrt{\sqrt 3^2+0+1^2}=\sqrt{4}=2, $$ $$\theta=\tan^{-1}( 0)=0, $$ $$\phi=\cos^{-1}(1/2)=\frac{\pi}{3}$$ Hence, the spherical coordinates are $(2,0,\frac{\pi}{3})$.
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