Answer
The rectangular coordinates of $\left( 2,\frac{\pi }{6} \right)$ are $\left( \sqrt{3},1 \right)$.
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,
$\begin{align}
& x=2\cos \frac{\pi }{6} \\
& =2\times \frac{\sqrt{3}}{2} \\
& =\sqrt{3}
\end{align}$
And
$\begin{align}
& y=2\sin \frac{\pi }{6} \\
& =2\times \frac{1}{2} \\
& =1
\end{align}$
Therefore, the rectangular coordinates of $\left( 2,\frac{\pi }{6} \right)$ are $\left( \sqrt{3},1 \right)$.
