Given polar coordinates,

\((4, 90^{\circ})\)

To find the rectangular coordinates of the point.

We have,

\((r, \theta) = (4, 90^{\circ})\)

Conversion formula :

If \((r, \theta)\)are polar coordinates and (x, y) are rectangular coordinates,

Then \(x = r cos \theta, y = r sin \theta\)

\(x = 4 cos(90^\circ) = 0\)

\(y = 4 sin(90^\circ) = 4(1) = 4\)

So the rectangular coordinates is (0, 4)

\((4, 90^{\circ})\)

To find the rectangular coordinates of the point.

We have,

\((r, \theta) = (4, 90^{\circ})\)

Conversion formula :

If \((r, \theta)\)are polar coordinates and (x, y) are rectangular coordinates,

Then \(x = r cos \theta, y = r sin \theta\)

\(x = 4 cos(90^\circ) = 0\)

\(y = 4 sin(90^\circ) = 4(1) = 4\)

So the rectangular coordinates is (0, 4)