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 699: 7

Answer

$(1, \sqrt 3,7) \Longrightarrow (2, \frac{\pi}{3},7) $.

Work Step by Step

We have $$ x=1, \quad y =\sqrt 3, \quad z=7.$$ Now, we have $$ r=\sqrt{x^2+y^2}=\sqrt{4}=2,$$ $$\theta =\tan^{-1}y/x=\tan^{-1}\frac{1}{\sqrt{3}}=\frac{\pi}{3}=\frac{\pi}{3},$$ $$ z=7.$$ So, $(1, \sqrt 3,7) \Longrightarrow (2, \frac{\pi}{3},7) $.
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