Prerequisites
• None

### Curves

!

Figure 1: The graph of a function of 1 variable.

There are many ways to describe a curve. Consider the following descriptions:

• the unit circle;
• $x^2+y^2=1$;
• $y=\sqrt{1-x^2}$;
• $r=1$;
• $x=\cos\phi$, $y=\sin\phi$;
• $\rr(\phi)=\cos\phi\,\xhat+\sin\phi\,\yhat$;
all of which describe (pieces of) the same curve. Here are some more:
• The graph of $y=x^2$;
• The figure shown at the right.
Which representation is best for a given problem depends on the circumstances.