Example 3: One cycle of the sine function

The parametric curve or trajectory for these parametric equations is one cycle of the function $y=\sin x$ .

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

This is another example where $x=f(t)$ is the identity function $x=t$ .

The parametric curve will be the same as the graph of $y=g(x)=\sin(x)$ .