Sine of the angle multiplied by the radius gives the Y axis position, cosine multiplied by the radius gives the X axis position from center depending on your own personal axis preferences of course.
If you require starting a hole pattern that is not at a right angle to your axes then just add the difference. As an example if one required a 4 hole bolt circle rotated 10 Deg. start a 10, calculate the next position at 100 Deg. then 190 Deg. and so on.