[Math] Distance Between Any Two Points on a Unit Circle

circlescomplex numbers

As part of a larger investigation, I am required to be able to calculate the distance between any two points on a unit circle. I have tried to use cosine law but I can't determine any specific manner in which I can calculate theta if the angle between the two points and the positive axis is always given.

Is there any manner in which I can do this?

Thanks

Best Answer

If the arc distance between the two points is $\theta$, the length of the chord between them is $2\sin\frac{\theta}{2}$:

geometry diagram