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\mathop{\rm hav}(z)\equiv {\textstyle{1\over 2}}\mathop{\rm vers}(z)={\textstyle{1\over 2}}(1-\cos z),

where $\mathop{\rm vers}(z)$ is the Versine and cos is the Cosine. Using a trigonometric identity, the haversine is equal to

\mathop{\rm hav}(z)=\sin^2({\textstyle{1\over 2}}z).

See also Cosine, Coversine, Exsecant, Versine


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

© 1996-9 Eric W. Weisstein