Example 1: The top half of the unit circle

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

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