Example 7: The unit circle

The parametric curve or trajectory for these parametric equations is the unit circle:

$$\left. \begin{array}{lclcl} x &=& f(t) &=& \cos t\\ y &=& g(t) &=& \sin t\\ \end{array}\right\}\quad 0\leq t\leq 2\pi$$

The only difference between this example and example 1 is that we let $t$ range from 0 to $2\pi$ , which produces the full unit circle.