Answer
The rectangular coordinates of $\left( 6,{{180}^{\circ }} \right)$ are $\left( -6,0 \right)$.
Work Step by Step
The rectangular coordinates of the point are $\left( x,y \right)$.
Now rewrite the rectangular coordinates in terms of polar coordinates,
$x=r\cos \theta \ \text{ and }\ y=r\sin \theta $ ……(I)
Substituting the values of $r\ \text{ and }\ \theta $ in (I) we get
$\begin{align}
& x=6\cos {{180}^{\circ }} \\
& =6\times \left( -1 \right) \\
& =-6
\end{align}$
And,
$\begin{align}
& y=6\sin {{180}^{\circ }} \\
& =6\times 0 \\
& =0
\end{align}$
Therefore, the rectangular coordinates of $\left( 6,{{180}^{\circ }} \right)$ are $\left( -6,0 \right)$.
