General formula of coordinates of a point on an arc given the centre of the arc, radius and the starting and ending angle of arc wrt horizontal.

Question

I am given the centre of an arc, the starting and ending angles of the arc wrt the horizontal and the radius of the arc.
I want a general formula that I can use to get the coordinates of points on the arc in terms of the radius, coordinates of the centre and the angles.

How do I calculate that?

Clarifying Image

Edit: The angle(s) do not necessarily have to be the starting or the ending angles. It is completely okay if the formula is a function of the angle of the line connecting the centre to that point on the arc instead. (Please refer to the Image in the link above for clarification)