Secret trigonometry

Hidden Trigonometry functions

The versine or versed sine is a trigonometric function found in some of the earliest (Vedic Aryabhatia I) trigonometric tables.
The versine of an angle is 1 minus its cosine.
There are several related functions, most notably the coversine and haversine.
The latter, half a versine, is of particular importance in the haversine formula of navigation
(source: Wikipedia)

vsin(Θ) = 1 - cos(Θ)

cvsin(Θ) = 1 - sin(Θ)

vcos(Θ) = 1 + cos(Θ)

cvcos(Θ) = 1 + sin(Θ)

hvsin(Θ) = (1 - cos(Θ)) / 2

hcvsin(Θ) = (1 - sin(Θ)) / 2

hvcos(Θ) = (1 + cos(Θ)) / 2

hcvcos(Θ) = (1 + sin(Θ)) / 2

Hidden Trigonometry calculus, derivates and integrals

Examples

```txt

derivates

d(vsin x) / dx = sin x d(cvsin x) / dx = -cos x

integrals

∫ vsin(x) dx = x - sin x + C ∫ cvsin(x) dx = x + cos x + C ```