Curves

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Section 4.3 Curves

Figure 4.3.1. 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 4.3.1.

Which representation is best for a given problem depends on the circumstances.