Versine

The versine, also known as the "versed sine," is a little-used trigonometric function defined by

			(1)
			(2)

where  is the sine and  is the cosine.

The versine can be extended to the complex plane as illustrated above.

Its derivative is given by

(3)

and its indefinite integral by

(4)

REFERENCES:

Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 78, 1972.