The haversine, written or , is a little-used trigonometric function defined by

			(1)
			(2)
			(3)

where is the versine and is the cosine.

The haversine is implemented in Mathematica as Haversine[z].

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

Its derivative is given by

(4)

and its indefinite integral by

(5)

It has Maclaurin series

			(6)
			(7)

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.

Smart, W. M. Text-Book on Spherical Astronomy, 6th ed. Cambridge, England: Cambridge University Press, p. 18, 1960.

CITE THIS AS:

Weisstein, Eric W. "Haversine." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Haversine.html