Answered: Convert the point (x, y, z) = (5, 3, -…

Convert the point (x, y, z) = (5, 3, - 1) to spherical coordinates. Give answers as positive values, either as expressions, or decimals to one decimal place. (p, 0, $) =

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter12: Conic Sections

Section12.6: Polar Equations Of Conics

Problem 45E

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Question

Convert the point (x, y, z) = (5, 3, 1) to spherical coordinates. Give answers as positive values,
either as expressions, or decimals to one decimal place.
(p, 0, $) =
cos (-1)
V52 + 32 + (-1)?
-1
99.731
735
COS

Expert Solution

Step 1

For converting Cartesian to spherical coordinates use the following expression,

p= $\sqrt{x^{2} + y^{2} + z^{2}}$

$θ = \tan^{- 1} \frac{y}{x}$

$ϕ = \tan^{- 1}$ $\frac{\sqrt{x^{2} + y^{2}}}{z}$

Substitute for x,y and z.

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