Answer
The rectangular coordinates of $\left( 4,{{90}^{\circ }} \right)$ are $\left( 0,4 \right)$.
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,
$\begin{align}
& x=4\cos {{90}^{\circ }} \\
& =4\times 0 \\
& =0
\end{align}$
And,
$\begin{align}
& y=4\sin {{90}^{\circ }} \\
& =4\times 1 \\
& =4
\end{align}$
Therefore, the rectangular coordinates of $\left( 4,{{90}^{\circ }} \right)$ are $\left( 0,4 \right)$.
