Cartesian coordinates for point on circle given angle from center

Question

I was wondering whether there is a simpler formula for finding the Cartesian Coordinates for a point on a circle given it's angle to the center and the radius. For example, if we have an angle of $90^\circ,$ the point would be at $(0, r)$, and if the angle was $45^\circ,$ we would get $\left(\frac{r\sqrt{2}}{2},\frac{r\sqrt{2}}{2}\right)$.