Why coordinate rotation matters
Parts do not always sit square on the table, and hole patterns or features are not always laid out along the machine axes. Rather than re-deriving every point on a rotated feature by hand, this rotates an entire set of X and Y coordinates about the origin by a given angle, which is exactly what happens internally when a control applies a coordinate system rotation.
How the numbers are calculated
The new X coordinate is the original X times the cosine of the rotation angle, minus the original Y times the sine of the angle. The new Y coordinate is the original X times the sine of the angle, plus the original Y times the cosine of the angle. This is the standard two-dimensional rotation transformation, with a positive angle representing counterclockwise rotation about the origin.
Practical tips
Make sure the point being rotated is expressed relative to the actual center of rotation before running this calculation, since the formula rotates about the origin, not about an arbitrary point. If a feature needs to rotate about a point other than zero, zero, subtract that center point from the coordinates first, rotate, then add the center point back in afterward.