   Chapter 15.8, Problem 1E

Chapter
Section
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 spherical coordinates and find the corresponding rectangular coordinates.

Explanation

Given:

The spherical coordinates (6,π3,π6) .

Formula used:

The rectangular coordinates (x,y,z) corresponding to the spherical coordinates (ρ,θ,ϕ) is,

x=ρsinϕcosθy=ρsinϕsinθz=ρcosϕ

Calculation:

The given spherical coordinates (6,π3,π6) plotted in the graph as shown below in the Figure 1.

From the Figure 1, it is observed that the point 6 in the x-axis is rotated anti-clockwise to the angle π3 and again rotated downwards from the z-axis at the angle of π6 .

From the given conditions, it is observed that ρ=6,θ=π3,ϕ=π6 . Therefore, by the formula mentioned above, the rectangular coordinates are obtained as follows

(b)

To determine

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

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