   Chapter 11.7, Problem 79E

Chapter
Section
Textbook Problem

# Rectangular and Cylindrical Coordinates Give the equation for the coordinate conversion from rectangular to cylindrical coordinates and vice versa.

To determine

The equations for the co-ordinates conversion form rectangular co-ordinate to cylindrical co-ordinates and vice-versa.

Explanation

Takecylindrical co-ordinates as (r,θ,z) and Rectangular co-ordinates as (x,y,z).

In a cylindrical co-ordinate system, a point P in space can be represented by an ordered triple (r,θ,z) Where, (r,θ) is a polar representation of the projection of P in the xy-plane and z is the directed distance from (r,θ) to P.

As shown in the figure,

Rectangular to cylindrical co-ordinate conversion:

Use the Pythagorean Theorem to calculate first co-ordinatewhich states that the square of the hypotenuse is equal to the sum of the squares of the perpendicular and the base.

This can be written as, a2=b2+c2

As shown in figure,

Therefore, the first co-ordinate with the help of Pythagorean Theoremis r2=x2+y2

### 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

#### Evaluate the expression sin Exercises 116. (2)3

Finite Mathematics and Applied Calculus (MindTap Course List)

#### Subtract the following numbers. 16.

Contemporary Mathematics for Business & Consumers

#### Multiply: (8)(4)

Elementary Technical Mathematics

#### Can the matrices in Problems 5-8 be transition matrices? If not, why? 5.

Mathematical Applications for the Management, Life, and Social Sciences

#### For f(x) = 6x4, f′(x) = _____. 24x 6x3 10x3 24x3

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 