Answer
The required ordered pair in Cartesian coordinates is $\left( \frac{3\sqrt{2}}{2},-\frac{3\sqrt{2}}{2} \right)$.
Work Step by Step
The Cartesian coordinates in the polar form are given by $x=r\,\cos \,\theta \ \ \text{ and }\ y=r\,\sin \,\theta $.
The provided data is $r=-3\ \text{ and }\ \theta =\frac{5\pi }{4}$.
Therefore, the required Cartesian coordinates are
$\begin{align}
& x=r\,\cos \,\theta \\
& x=-3\,\cos \left( \frac{5\pi }{4} \right) \\
& x=\frac{3\sqrt{2}}{2}
\end{align}$
and
$\begin{align}
& y=r\,\sin \,\theta \\
& y=-3\,\sin \left( \frac{5\pi }{4} \right) \\
& y=-\frac{3\sqrt{2}}{2}
\end{align}$
Therefore, the required Cartesian coordinates are $\left( \frac{3\sqrt{2}}{2},-\frac{3\sqrt{2}}{2} \right)$.
