What are the versed sine and coversed sine of an angle?

[Miike012]

Homework Statement

The quantity by which the cosine falls short of unity. Ie: 1-cos angle AOP is called the versed sine of AOP.
The quantity 1-sin AOP by which the sine falls short of unity is called the coversed sine of AOP..
HUH? Falls short of what?

 

[eumyang]

Homework Statement

The quantity by which the cosine falls short of unity. Ie: 1-cos angle AOP is called the versed sine of AOP.
The quantity 1-sin AOP by which the sine falls short of unity is called the coversed sine of AOP..
HUH? Falls short of what?

Falls short of unity, and unity means the number one, of course. The versed sine (or versine) of an angle is the difference of 1 and the cosine of that angle.

versin 30° = 1 - cos 30° ≈ 1 - 0.866 ≈ 0.134

The coversed sine (coversine) of an angle is the difference of 1 and the sine of that angle.
coversin 30° = 1 - sin 30° = 1 - 0.5 = 0.5

BTW, the versine isn't used much these days. See http://en.wikipedia.org/wiki/Versine" .