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1Mathematics The ratio of the hypotenuse to the shorter side adjacent to an acute angle (in a right-angled triangle); the reciprocal of a cosine.
‘The secant of this angle is 1.61806 which is remarkably close to the golden ratio 1.618034.’
‘He gave a table of secants and, although Delambre credited him with the first use of this function, it had appeared earlier in the work of Copernicus.’
‘When you move the cursor over a button on the calculator, a description of its function appears - sine of a number, cosine, secant, etc.’
‘The secant and cosecant were not used by the early astronomers or surveyors.’
‘It also gave tables of natural sine functions to 15 decimal places, and the tan and sec functions to 10 decimal places.’
2Geometry A straight line that cuts a curve in two or more parts.
‘Direct irradiance was attenuated as described by Beer's law, with the optical path length increasing approximately as the secant of the solar zenith angle.’
‘Note that the air mass is approximately equal to the secant of the zenith angle (that angle from directly overhead to a line intersecting the sun).’
‘In this projection the meridians are vertical and parallels having increased spacing in proportion to the secant of the latitude.’
Origin
Late 16th century; from French sécante, based on Latin secare ‘to cut’.