Answer
The required ordered pair in polar coordinates is $\left( 6,\pi \right)$.
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 $x=-6\ \text{ and }\ y=0$.
Therefore, we can determine the required polar coordinates by using the following formulas:
$r=\sqrt{{{y}^{2}}+{{x}^{2}}}\ \text{ and }\ \text{tan}\,\theta =\frac{y}{x}$
Therefore, the polar coordinate r is given by:
$\begin{align}
& r=\sqrt{{{y}^{2}}+{{x}^{2}}} \\
& =\sqrt{{{\left( -6 \right)}^{2}}+{{0}^{2}}} \\
& =\text{6}
\end{align}$
and
$\begin{align}
& \text{tan}\,\theta =\frac{y}{x} \\
& =\frac{0}{-6} \\
& =0
\end{align}$
Therefore, $\theta =\pi $.
Thus, the required polar coordinates are $\left( r,\theta \right)=\left( 6,\pi \right)$.
