Answer
To convert a point from rectangular to polar coordinates or from $\left( x,y \right)$ to $\left( r,\theta \right)$ we will use the formula $r=\sqrt{{{x}^{2}}+{{y}^{2}}}$, for determining the value of r, and
$\tan \theta =\frac{y}{x}$, for determining the value of $\theta $.
Work Step by Step
For example, consider a point $\left( 1,\sqrt{3} \right)$. It can be converted into polar coordinates as,
$\begin{align}
& r=\sqrt{{{1}^{2}}+{{\left( \sqrt{3} \right)}^{2}}} \\
& =\sqrt{1+3} \\
& =\sqrt{4} \\
& =2
\end{align}$
$\begin{align}
& \tan \theta =\frac{\sqrt{3}}{1} \\
& \theta ={{\tan }^{-1}}\left( \sqrt{3} \right) \\
& =\frac{\pi }{3}
\end{align}$
Hence, the rectangular point $\left( 1,\sqrt{3} \right)$ becomes $\left( 2,\frac{\pi }{3} \right)$ in polar coordinates.
