   Chapter 15.7, Problem 2E

Chapter
Section
Textbook Problem

Plot the point whose cylindrical coordinates are given. Then find the rectangular coordinates of the point.2. (a) ( 2 ,   3 π / 4 ,     2 ) (b) (1, 1, 1)

(a)

To determine

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

Explanation

Given:

The cylindrical coordinates (2,3π4,2) .

Formula used:

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

x=rcosθy=rsinθz=z

Calculation:

The given cylindrical coordinates (2,3π4,2) plotted in the graph as shown below in the Figure 1.

From the Figure 1, it is observed that the point 2 in the x-axis is rotated to the angle 3π4 and raise to the z-axis by the height of 2.

From the given conditions, it is observed that r=2,θ=3π4,z=2 . Therefore, obtain the required coordinates by using the formula mentioned above.

Compute the x-coordinate as follows

(b)

To determine

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

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