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Section 6.3 Curves

Figure 6.3.1. The graph of a functions of 1 variable.

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.