>The second one combines quantities that I never before even
>saw used.

It appears the quantity is well known and is called versine (as a piece of since rotated 90°).

If AB is a segment in a (unit) circle with center O and midpoint M. If angle AOM = α and the radius through M is OS, then MS is the versine of α:
 

MS= vers(α)
MS= 1 - cos(α)
MS= 2·sin2(α/2).



I ran into this term in an article in Math Horizons (Sept., 2006).

Here's a hole in my education.