Definitions
from The American Heritage® Dictionary of the English Language, 5th Edition.
 noun A straight line intersecting a curve at two or more points.
 noun The straight line drawn from the center through one end of a circular arc and intersecting the tangent to the other end of the arc.
 noun The ratio of the length of this line to the length of the radius of the circle.
 noun The reciprocal of the cosine of an angle in a right triangle.
from The Century Dictionary.
 Cutting; dividing into two parts.
 noun A line which cuts a figure in any way.
 noun Specifically, in trigonometry, a line from the center of a circle through one extremity of an are (whose secant it is said to be) to the tangent from the other extremity of the same are; or the ratio of this line to the radius; the reciprocal of the cosine.
 Specifically, noting a stream which cuts across folded strata.
from the GNU version of the Collaborative International Dictionary of English.
 adjective Cutting; dividing into two parts.
 noun (Geom.) A line that cuts another; especially, a straight line cutting a curve in two or more points.
 noun (Trig.) A right line drawn from the center of a circle through one end of a circular arc, and terminated by a tangent drawn from the other end; the number expressing the ratio of this line to the radius of the circle. See Trigonometrical function, under
Function .
from Wiktionary, Creative Commons Attribution/ShareAlike License.
 noun geometry A
straight line thatintersects acurve at two or morepoints .  noun trigonometry In a
right triangle , thereciprocal of thecosine of anangle . Symbol:sec
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 noun ratio of the hypotenuse to the adjacent side of a rightangled triangle
 noun a straight line that intersects a curve at two or more points
Etymologies
from The American Heritage® Dictionary of the English Language, 4th Edition
from Wiktionary, Creative Commons Attribution/ShareAlike License
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Examples

So: why is the word secant used as the word for the reciprocals of sine and cosine? what is the perimeter of a rhombus who's diagonals are 8 and 22? en Español

Why is the word secant used as the word for the reciprocals of sine and cosine? en Español

why is the word secant used as the word for the reciprocals of sine and cosine? what is the perimeter of a rhombus who's diagonals are 8 and 22? en Español

The secant is the reciprocal of the cosine, the cosecant is the reciprocal of the sine, and the cotangent is the reciprocal of the tangent.
Citizendium, the Citizens' Compendium  Recent changes [en] 2008

"One secant," he said, giggling and walking faster through the swarming crowd.
Marc Philippe Eskenazi: Eavesdropping on New York Cell Phone Conversations Marc Philippe Eskenazi 2011

"One secant," he said, giggling and walking faster through the swarming crowd.
Marc Philippe Eskenazi: Eavesdropping on New York Cell Phone Conversations Marc Philippe Eskenazi 2011

One with secant ogive and minimal meplat is best at extreme distances such as 1000 yards.

"One secant," he repeated as his brain waves began brawling.
Marc Philippe Eskenazi: Eavesdropping on New York Cell Phone Conversations Marc Philippe Eskenazi 2011

One with secant ogive and minimal meplat is best at extreme distances such as 1000 yards.

"One secant," he repeated as his brain waves began brawling.
Marc Philippe Eskenazi: Eavesdropping on New York Cell Phone Conversations Marc Philippe Eskenazi 2011
chained_bear commented on the word secant
"Few understood the Rule of Three; few could multiply with any certainty, nor yet divide; none knew the nature of a logarithm, a secant, a sine."
"'...What do you make of it?'
Patrick O'Brian, The Ionian Mission, 120
February 13, 2008