Section 6.3 Curves
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There are many ways to describe a curve. Consider the following descriptions:
The unit circle;
\(x^2+y^2=1\text{;}\)
\(y=\sqrt{1-x^2}\text{;}\)
\(r=1\text{;}\)
\(x=\cos\phi\text{,}\) \(y=\sin\phi\text{;}\)
\(\rr(\phi)=\cos\phi\,\xhat+\sin\phi\,\yhat\text{;}\)
all of which describe (pieces of) the same curve. Here are some more:
The graph of \(y=x^2\text{;}\)
The graph shown in Figure 6.3.1.
Which representation is best for a given problem depends on the circumstances.