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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

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Chapter
Section
BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

Plot the point whose cylindrical coordinates are given. Then find the rectangular coordinates of the point.

1. (a) (4, π /3, –2)

(b) (2, – π /2. 1)

(a)

To determine

To plot: The given cylindrical coordinates and find the corresponding rectangular coordinates.

Explanation

Formula used:

The rectangular coordinates (x,y,z) corresponding to the cylindrical coordinates (r,θ,z) is,

x=rcosθy=rsinθz=z

Given:

The cylindrical coordinates (4,π3,2) .

Calculation:

The given cylindrical coordinates (4,π3,2) plotted in the graph as shown below in the Figure 1.

From the Figure 1, it is observed that the point 4 in the x-axis is rotated to the angle π3 and raise to the z-axis by the height of 2

(b)

To determine

To plot: The given cylindrical coordinates and find the corresponding rectangular coordinates.

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Chapter 15 Solutions

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