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Chapter 6: Problem 77

Use a graphing utility to graph the curve represented by the parametric equations. Cycloid: \(x=4(\theta-\sin \theta), y=4(1-\cos \theta)\)

Short Answer

Expert verified
The graph of the given parametric equations represents a curve known as 'Cycloid' which looks like a series of arches or 'wheel-like' curve.

Step by step solution

01

Understand the parametric equations

In the provided Cycloid parametric equations, \(x\) and \(y\) are both written in terms of the parameter \(\theta\). These equations describe a curve in the \(xy\)-plane as \(\theta\) varies.
02

Prepare to graph

To graph these equations, input values for \(\theta\) and calculate the resulting \(x\) and \(y\) for each value of \(\theta\). The choice of \(\theta\) values should be such that they are evenly spaced within one full cycle of the sine and cosine functions, say from \(\theta = -2\pi\) to \(\theta = 2\pi\).
03

Graph the Curve

Plot each pair of \(x\) and \(y\) values in a coordinate system. Connect these points smoothly to create the graph of the curve described by the parametric equations.

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