   Chapter 15, Problem 11RE

Chapter
Section
Textbook Problem

The cylindrical coordinates of a point are ( 2 3 , π 3 , 2). Find the rectangular and spherical coordinates of the point.

To determine

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

Explanation

Formula used:

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

x=rcosθy=rsinθz=z (1)

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

ρ=x2+y2+z2ϕ=cos1(zρ)θ=cos1(xρsinϕ) (2)

Given:

The cylindrical coordinates (23,π3,2) .

Calculation:

From the given conditions, it is observed that r=23,θ=π3,z=2 . Therefore by the formula (1) mentioned above,

x=rcosθ=23cos(π3)=23(12)=3

y=23sin(π3)=2332=3

z=z=2

The rectangular coordinates is given by, (3,3,2)

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Find more solutions based on key concepts 