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Versine

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Versine

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

versin(z)=2sin^2(1/2z)
(1)
=1-cosz,
(2)

where sinz is the sine and cosz is the cosine.

VersineReIm
VersineContours

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

Its derivative is given by

d/(dz)vers(z)=sinz,
(3)

and its indefinite integral by

intvers(z)dz=z-sinz+C.
(4)

See also

Covercosine, Coversine, Excosecant, Exsecant, Hacovercosine, Hacoversine, Havercosine, Haversine, Sine, Vercosine

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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.

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Versine

Cite this as:

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

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