   Chapter 10, Problem 34RE

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 = 5 sin 3 θ ,   y = 5 cos 3 θ

To determine

To calculate: The corresponding rectangular equation by eliminating the parameters and plot the graph of the rectangular equation for the parametric equations x=5sin3θ, y=5cos3θ.

Explanation

Given:

The parametric equation are x=5sin3θ, y=5cos3θ.

Calculation:

Consider the parametric equations:

x=5sin3θ

y=5cos3θ

To graph the function follow the steps:

Step 1: Press the MODE key

Step 2: Select the option Par

Step3: Press the key Y=

Step4: Write Y1=5sin3t and Y2=5cos3t

Step5: Press the GRAPH key

The graph representing these equations is obtained as below:

Rewrite the given equations as:

x5=sin3θ

y5=cos3θ

On finding the cube root:

sinθ=(x5)1/3

cosθ=

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