   Chapter 15.8, Problem 2E

Chapter
Section
Textbook Problem

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

(a)

To determine

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

Explanation

Given:

The spherical coordinates (2,π2,π2) .

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 (2,π2,π2) 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 anti clockwise to the angle π2 and again rotated downwards from the z-axis at the angle of π2 .

From the given conditions, it is observed that ρ=2,θ=π2,ϕ=π2

(b)

To determine

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

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