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Chapter 6: Problem 83

Use a graphing utility to graph the curve represented by the parametric equations. Hypocycloid: \(x=3 \cos ^{3} \theta, y=3 \sin ^{3} \theta\)

Short Answer

Expert verified
Inserting \(x=3 \cos ^{3} \theta\) and \(y=3 \sin ^{3} \theta\) into a graphing tool and plotting should yield a curve that is symmetrical and resembles a three-leaf clover.

Step by step solution

01

Understand the equations

Parametric equations use a parameter, in this case \(\theta\), to represent the coordinates x and y. We have the parametric equations \(x=3 \cos ^{3} \theta\) and \(y=3 \sin ^{3} \theta\).
02

Insert equations into the graphing tool

Most graphing utilities or software have an option for graphing parametric equations. The \(\cos^{3} \theta\) and \(\sin^{3} \theta\) functions have to be plugged in the x and y inputs respectively.
03

Analyze the graph

Once you obtain the graph, analyze it by observing the shape and characteristics of the curve. The hypocycloid curve should form a shape similar to a three-leaf clover. It should be symmetrical with reference to the origin.

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