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Exsecant

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Exsecant

The exsecant is a little-used trigonometric function defined by

exsec(x)=secx-1,
(1)

where secx is the secant.

ExsecantReIm
ExsecantContours

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

Its derivative is given by

d/(dz)exsec(z)=secztanz,
(2)

and its indefinite integral by

intexsec(z)dz=ln[cos(1/2z)+sin(1/2z)] -ln[cos(1/2z)-sin(1/2z)]-z+C.
(3)

See also

Covercosine, Coversine, Excosecant, Hacoversine, Havercosine, Haversine, Secant, Vercosine, Versine

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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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Exsecant

Cite this as:

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

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