Consider a circle of radius $4$ centered at the origin in the $xy$-plane. Find a parametrization for the arc of this circle that lies in the fourth quadrant and has clockwise orientation. The point $(4,0)$ should correspond to $t = 0$ and the point $(0,-4)$ should correspond to the right endpoint of the interval of $t$ values.

$\vec{r}(t) =$ for $0 \leq t \leq$

Note: Use $t$ as the parameter for all of your answers and write $\vec{r}(t)$ in the form $< x(t), y(t) >$ without using $\vec{i}$ and $\vec{j}$. In order to have your answer checked for correctness, you must have answers in both answer blanks.