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.

Related Topics:
Surveying - Astronomy - Spherical trigonometry - Calculator - Computer

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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:

Related Topics:
Versine - Angle - One - Subtraction - Floating point

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

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