   Chapter 15, Problem 12RE

Chapter
Section
Textbook Problem

The rectangular coordinates of a point are (2, 2, −1). Find the cylindrical and spherical coordinates of the point.

To determine

To find: The corresponding cylindrical and spherical coordinates for the given rectangular 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 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 rectangular coordinates (2,2,1) .

Calculation:

From the given conditions, it is observed that x=2,y=2,z=1 .

Obtain the cylindrical coordinates by the formula (1) mentioned above.

r=(2)2+(2)2=4+4=8=22

θ=tan1(22)

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 the limit. limxx292x6

Single Variable Calculus: Early Transcendentals, Volume I

Solve the equations in Exercises 126. x+4x+1+x+43x=0

Finite Mathematics and Applied Calculus (MindTap Course List)

In Exercises 33-38, rewrite the expression using positive exponents only. 33. (xy)2

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Evaluate the integrals in Problems 1-11.

Mathematical Applications for the Management, Life, and Social Sciences 