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Chapter 6: Problem 52

Use a graphing utility to graph the curve represented by the parametric equations. Prolate cycloid: \(x=2 \theta-4 \sin \theta, y=2-4 \cos \theta\)

Short Answer

Expert verified
The graph of the given parametric equations forms a prolate cycloid, which resembles a series of wave-like patterns.

Step by step solution

01

Open the graphing utility

First, open up the graphing utility of your choice. This could be a physical graphing calculator or an online tool.
02

Input the equations

In the tool's function input section, enter the two given equations \(x = 2\theta - 4\sin(\theta)\) and \(y = 2 - 4\cos(\theta)\). You should input each equation exactly as it is written, with \(\theta\) representing the parameter or variable input.
03

Set range for theta

Set a range for the parameter \(\theta\). A standard choice could be from 0 to 2\(\pi\) which means the graph will represent one complete cycle of the parametric curve.
04

Create the plot

After entering the equations and setting a range for the parameter \(\theta\), generate the plot. This should create a visual representation of the parametric equations, which represents a prolate cycloid.
05

Analyze the graph

Now, inspect the generated plot. The shape you should see is a prolate cycloid, which resembles a series of arches or wave-like patterns.

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