Parametric Curve - Parametric Equations & Polar Coordinates

Here now, let us take a look at just how we could probably get two tangents lines at a point.  This was surely not possible back in Calculus I where we first ran across tangent lines.

A quick graph of the parametric curve will illustrate what is going on here.

Thus, the parametric curve crosses itself!  That illustrates how there can be much more than one tangent line.  There is one tangent line for each example that the curve undergoes the point.