Answer
To convert a point from polar to rectangular coordinates or from $\left( r,\theta \right)$ to $\left( x,y \right)$, use one or more of the following identities:
$x=r\cos \theta $
$y=r\sin \theta $
Work Step by Step
To convert a point from polar coordinates to rectangular coordinates or from $\left( r,\theta \right)$ to $\left( x,y \right)$, we will use one or more of the following identities:
$x=r\cos \theta $
$y=r\sin \theta $
For example, consider a point $\left( 2,\frac{\pi }{3} \right)$. It can be converted into rectangular coordinates as below:
$\begin{align}
& x=2\cos \frac{\pi }{3} \\
& =2\cdot \frac{1}{2} \\
& =1
\end{align}$
$\begin{align}
& y=2\sin \frac{\pi }{3} \\
& =2\cdot \frac{\sqrt{3}}{2} \\
& =\sqrt{3}
\end{align}$
Hence, the polar point $\left( 2,\frac{\pi }{3} \right)$ becomes $\left( 1,\sqrt{3} \right)$ in rectangular coordinates.
