Exsecant

The exsecant, also abbreviated exsec, is a trigonometric function defined in terms of the secant function sec(θ):

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: extrm{exsec}( heta) = sec( heta) - 1 ,.

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Once important in fields such as surveying, astronomy, and spherical trigonometry, the exsecant function is now little-used. Mainly, this is because the availability of calculators and computers has removed the need for trigonometric tables of specialized functions such as this one.

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The reason to define a special function for the exsecant is similar to the rationale for the versine: for small angles θ, the sec(θ) function approaches one, and so using the above formula for the exsecant will involve the subtraction of two nearly equal quantities and exacerbate roundoff errors. Thus, a table of the secant function would need a very high accuracy to be used for the exsecant, making a specialized exsecant table useful. Even with a computer, floating point errors can be problematic for exsecants of small angles. A more accurate formula in this limit would be to use the identity:

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: extrm{exsec}( heta) = rac{1-cos( heta)}{cos( heta)}

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Surveying: Surveying is the art and science of accurately determining the position of points and the distances between them. These points are usually, but not exclusively, associated with positions on the surface of the Earth, and are often used to establish land boundaries for ownership or governmental purpo...

Astronomy: :This article is about the science branch. For information about the magazine, see Astronomy (magazine)....

Spherical trigonometry: Spherical trigonometry is a part of spherical geometry that deals with polygons (especially triangles) on the sphere and explains how to find relations between the involved angles. This is of great importance for calculations in astronomy and earth-surface and orbital and space navigation....