# secant

[see-kant, -kuh nt] /ˈsi kænt, -kənt/
noun
1.
Geometry. an intersecting line, especially one intersecting a curve at two or more points.
2.
Trigonometry.
1. (in a right triangle) the ratio of the hypotenuse to the side adjacent to a given angle.
2. (originally) a line from the center of a circle through one extremity of an arc to the tangent from the other extremity.
3. the ratio of the length of this line to that of the radius of the circle; the reciprocal of the cosine of a given angle or arc.
Abbreviation: sec.
3.
cutting or intersecting, as one line or surface in relation to another.
Origin of secant
1585-1595
1585-95; < Latin secant- (stem of secāns, present participle of secāre to cut), equivalent to sec- verb stem (see saw1) + -ant- -ant
Related forms
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2016.
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Examples from the Web for secant
Historical Examples
• If the curve has a tangent at P the secant PP′ approaches a limiting position (see 33 below).

• The complement of the logarithm of a sine, tangent, or secant.

William Henry Smyth
• secant equals one over cosine—um-m-m-m—one point oh three five.

Edward Elmer Smith
• The oblongs made of any secant from the same point, and of the outter segment of the secant are equall betweene themselves.

Peter Ramus
• That which is made by a right line, whether tangent or secant, with the circumference of a circle.

William Henry Smyth
• On any secant of an hyperbola the segments between the curve and the asymptotes are equal.

• The fraction Δy/Δx is the trigonometrical tangent of the angle which the secant PP′ makes with the axis of x.

• There is no necessary connexion between a conical projection and any touching or secant cone.

• The whole secret of avoiding shipwreck is to try and pass from the secant to the tangent.

Victor Hugo
• Every ray through S1 or S2 which is not a secant determines one of them.

British Dictionary definitions for secant

## secant

/ˈsiːkənt/
noun
1.
(of an angle) a trigonometric function that in a right-angled triangle is the ratio of the length of the hypotenuse to that of the adjacent side; the reciprocal of cosine sec
2.
a line that intersects a curve
Derived Forms
Word Origin
C16: from Latin secāre to cut
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012
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Word Origin and History for secant
n.

1590s, from Latin secantem (nominative secans) "a cutting," present participle of secare "to cut" (see section (n.)). First used by Danish mathematician Thomas Fincke in "Geometria Rotundi" (1583).

Online Etymology Dictionary, © 2010 Douglas Harper
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secant in Science
 secant   (sē'kānt')    A straight line or ray that intersects a curve, especially a circle, at two or more points.The ratio of the length of the hypotenuse in a right triangle to the side adjacent to an acute angle. The secant is the inverse of the cosine.The reciprocal of the abscissa of the endpoint of an arc of a unit circle centered at the origin of a Cartesian coordinate system, the arc being of length x and measured counterclockwise from the point (1, 0) if x is positive or clockwise if x is negative.A function of a number x, equal to the secant of an angle whose measure in radians is equal to x.
The American Heritage® Science Dictionary
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