+8  A: 

Let the fixed distance be D, then X = D * cos(A) and Y = D * sin(A), where A is the angle.

PolyThinker
+1  A: 
t = angle
r = radius (fixed distance)

x = rcost
y = rsint
Jason Punyon
+1  A: 

What PolyThinker said.

Also, if you need the distance from the origin, it's sqrt(x^2 + y^2).

Ben Alpert
+3  A: 

If center-point (Xcp, Ycp) isn't the origin you also need to add it's coordinates to (X,Y) i.e. X = Xcp + D * cos(A) and Y = Ycp + D * sin(A)

jeffD