Calculus (3rd Edition)

In the parametric curve $(t,\sin t)$ we have $x = t$ and $y = \sin t$, therefore, $y = sin x$. That is, the curve can be represented as a graph of a function. But in the parametric curve $(\sin t,t)$ we have $x = \sin t$ and $y = t$, therefore, $x = sin y$. This equation does not define $y$ as a function of $x$, therefore the parametric curve $(\sin t,t)$ cannot be represented as a graph of a function $y = f (x)$.