Answer
The required ordered pair in Cartesian coordinates is $\left( 0,-6 \right)$.
Work Step by Step
The Cartesian coordinates in polar form are given by $x=r\,\cos \,\theta \ \ \text{ and }\ y=r\,\sin \,\theta $.
The provided data is $r=6\ \text{ and }\ \theta =-\frac{\pi }{2}$.
Therefore, the required Cartesian coordinates are
$\begin{align}
& x=r\,\cos \,\theta \ \\
& x=6\,\cos \left( -\frac{\pi }{2} \right) \\
& x=6\,\cos \left( \frac{\pi }{2} \right) \\
& x=0
\end{align}$
and
$\begin{align}
& y=r\,\sin \,\theta \\
& y=6\,\sin \left( \frac{-\pi }{2} \right) \\
& y=-6
\end{align}$
Therefore, the required Cartesian coordinates are $\left( 0,-6 \right)$.
