# Math Insight

### Applet: Graph of a function that parametrizes an ellipse

Graph of the vector-valued function $\adllp(t)=(3\cos \frac{t^2}{2\pi})\vc{i} + (2 \sin \frac{t^2}{2\pi}) \vc{j}$. This function parametrizes an ellipse. Its graph, however, is the set of points $(t,3\cos \frac{t^2}{2\pi},2 \sin \frac{t^2}{2\pi})$, which forms a curve that spirals more quickly with increasing $t$.