   Chapter 10, Problem 31RE

Chapter
Section
Textbook Problem

# Using Parametric Equations In Exercises 27-34, sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter. x = 6 cos θ ,   y = 6 sin θ

To determine

To calculate: The corresponding rectangular equation by eliminating the parameters and plot the rectangular equation for the parametric equations x=6cosθ, y=6sinθ.

Explanation

Given:

The parametric equations are x=6cosθ, y=6sinθ.

Calculation:

Consider the given parametric equations.

x=6cosθ

y=6sinθ

To graph the parametric first find some values of x and y for different values of t.

For θ=0

x=6cos0=6y=6sin0=0

For θ=π2

x=6cosπ2=0y=6sinπ2=6

For θ=π

x=6cosπ=6y=6sinπ=0

For θ=3π2

x=6cos3π2=0y=6sin3π2=6

For θ=2π

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