Assuming you mean a unit circle with center at the origin, there are an infinite number of coordinate pairs on its circumference. The equation for the unit circle is:
x2 + y2 = 1 and anycombination of (x,y) values that makes true will be your answer.
The only integer answers are (1,0); (0,1); (-1,0) and (0,-1).
Other solutions involve 'special angles' in trig but have Irrational Numbers and or fractions.
300 --> (1/2 , [sq root 3] / 2)
450 --> ([sq root 2] / 2 , [sq root 2] / 2)
600 --> ([sq root 3] / 2 , 1/2)
any combinations of the above with opposite signs will also create coordinates for the unit circle.
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All complex number that can be represented by the coordinates of points on the unit circle, that is, the circle with its centre at the origin and a radius of 1 unit.
You can completely specify a circle in a plane by giving the coordinates of its center point, and the length of the radius.
Knowing two points on a circle does not define a unique circle, so it is impossible to find the centre of the circle as there are infinitely many centres possible.
(x-1, y)
Work out the length of the coordinates and half it.