## Precalculus (6th Edition) Blitzer

The rectangular coordinates of $\left( 4,{{90}^{\circ }} \right)$ are $\left( 0,4 \right)$.
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 $\left( 0,4 \right)$.