versine(A) = 2*sin^2(A/2) = 1 - cos(A)

The following is an attempt to describe versine. It is much easier to follow the description if you sketch it.

In a circle with radius = 1 consider a radius inclined at A degrees to the horizontal.

If the radius meets the circumference at P(x, y) then x = cos(A) and y=sin(A).

Then versine A is the distance from the point, on the x-axis, below P to the point where the circle meets the x-axis.

i got this off another persons question but it is nearly the exact same question.

1. HE USED LETTERS FOR UNKNOWN QUANTITIES.
2. WORKED ON THE APPROXIMATION OF "PI" TO 4 DECIMAL PLACES AND DEFINED IT AS IRRATIONAL.
3. GAVE THE AREA OF TRIANGLE AND CIRCLE.
4. DEFINED SINE, COSINE, VERSINE AND INVERSE SINE.