Example 9: The unit circle, twice around counterclockwise

The parametric curve or trajectory for these parametric equations is the unit circle, this time traced twice counterclockwise as $t$ varies from 0 to $2\pi$ .

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

This time we let $t$ vary from 0 to $2\pi$ , but we use $\cos 2t$ and $\sin 2t$ .

This trajectory will traverse the unit circle twice in the counterclockwise direction.