   Chapter 15, Problem 13RE

Chapter
Section
Textbook Problem

The spherical coordinates of a point are (8, π/4, π/6). Find the rectangular and cylindrical coordinates of the point.

To determine

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

Explanation

Formula used:

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

r=x2+y2θ=tan1(yx)z=z (1)

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

x=ρsinϕcosθy=ρsinϕsinθz=ρcosϕ (2)

Given:

The spherical coordinates (8,π4,π6) .

Calculation:

From the given conditions, it is observed that ρ=2,θ=π4,ϕ=π6 .

Then, by the formula (2) mentioned above, the x- value is,

x=ρsinϕcosθ=8sinπ6cosπ4=8(12)(12)=22

The y- value is,

y=ρsinϕsinθ=8sinπ6sinπ4=

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