Let say I have a circle with a known circumference that has arbitrary points on it around the circle. I want to convert/unravel that circle to a line segment and know where the arbitrary points on the circle reside on the line segment.

So for example, if a circle with a circumference of 10 is centered at (0,0) and has four total points that I care about every 90 degrees starting at 0 degrees. Then the circle is converted to a line segment along the X axis, what would the coordinates of the points that were on the circle now be on the line segment? I'm looking for a repeatable formula.

Thanks in advance for any help.