   Chapter 11, Problem 75RE

Chapter
Section
Textbook Problem

# Cylindrical-to-Rectangular Conversion In Exercises 75 and 76, find an equation in rectangular coordinates for the equation given in cylindrical coordinates, and sketch its graph. r = 5 cos θ

To determine

To calculate: The equation in rectangular coordinates for the equation r=5cosθ in cylindrical coordinates and to sketch its graph.

Explanation

Given:

The equation in cylindrical coordinates is r=5cosθ.

Formula used:

The conversion equations to convert a point (r,θ,z) in cylindrical coordinate to rectangular coordinate (x,y,z):

x=rcosθy=rsinθz=z

Calculation:

Consider the equation in cylindrical coordinate,

r=5cosθ

Multiply both the sides of the equation with r to get,

r2=5rcosθ

As,rcosθ=x and r2=x2+y2

Therefore,

x2+y2=5x

The above equation represents a circle. Convert the above equation of the circle in general form of the circle that is x2+y2=r2

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