I have a table of sin and cos values.
I know that the radius of the cirlce is 1. The center is 0.
I'm trying to figure out the CHORD length between the points on the circumference.
E.g. of points on the circle (cos,sin), (.5,-.87), (.87,.5), (.87,-.5)
Nt: I don't have center angle, I don't have arc length
Of course, one can just use the distance formula, $$d((x_1, y_1), (x_2, y_2)) = (x_2 - x_1)^2 + (y_2 - y_1)^2.$$
Alternatively, we can use this to produce a formula that calculates distance specifically between points on the unit circle:
If we regard the points on the unit circle as vectors ${\bf x}, {\bf y}$, the distance formula is $$d({\bf x}, {\bf y}) = |{\bf x} - {\bf y}|.$$
Now, $$\phantom{(\ast)} \qquad |{\bf x} - {\bf y}|^2 = ({\bf x} - {\bf y}) \cdot ({\bf x} - {\bf y}) = {\bf x} \cdot {\bf x} - 2 {\bf x} \cdot {\bf y} + {\bf y} \cdot {\bf y} , \qquad (\ast)$$ and since ${\bf x}, {\bf y}$ are on the unit circle, we have after factoring that $$|{\bf x} - {\bf y}|^2 = 2 (1 - {\bf x} \cdot {\bf y}),$$ so $$d({\bf x}, {\bf y}) = \sqrt{2 (1 - {\bf x} \cdot {\bf y})}.$$
(Note, by the way, that $(\ast)$ is just the usual Law of Cosines.)