Geometry. a line or a plane that touches a curve or a surface at a point so that it is closer to the curve in the vicinity of the point than any other line or plane drawn through the point.

Trigonometry.

(in a right triangle) the ratio of the side opposite a given angle to the side adjacent to the angle.

Also called tan.(of an angle) a trigonometric function equal to the ratio of the ordinate of the end point of the arc to the abscissa of this end point, the origin being at the center of the circle on which the arc lies and the initial point of the arc being on the x-axis. Abbreviation: tg, tgn

(originally) a straight line perpendicular to the radius of a circle at one end of an arc and extending from this point to the produced radius which cuts off the arc at its other end.

the upright metal blade, fastened on the inner end of a clavichord key, that rises and strikes the string when the outer end of the key is depressed.

Idioms

off on/at a tangent, digressing suddenly from one course of action or thought and turning to another: The speaker flew off on a tangent.

Origin of tangent

1585–90; < Latintangent- (stem of tangēns, present participle of tangere to touch) in phrase līnea tangēns touching line; see -ent

a geometric line, curve, plane, or curved surface that touches another curve or surface at one point but does not intersect it

(of an angle) a trigonometric function that in a right-angled triangle is the ratio of the length of the opposite side to that of the adjacent side; the ratio of sine to cosineAbbreviation: tan

the straight part on a survey line between curves

musica part of the action of a clavichord consisting of a small piece of metal that strikes the string to produce a note

on a tangentorat a tangenton a completely different or divergent course, esp of thoughtto go off at a tangent

adjective

of or involving a tangent

touching at a single point

touching

almost irrelevant

Derived Formstangency, noun

Word Origin for tangent

C16: from Latin phrase līnea tangēns the touching line, from tangere to touch

1590s, "meeting at a point without intersecting," from Latin tangentem (nominative tangens), present participle of tangere "to touch," from PIE root *tag- "to touch, to handle" (cf. Latin tactus "touch," Greek tetagon "having seized," Old English þaccian "stroke, strike gently"). First used by Danish mathematician Thomas Fincke in "Geomietria Rotundi" (1583). Extended sense of "slightly connected with a subject" is first recorded 1825. The noun also is attested from 1590s.

A line, curve, or surface touching but not intersecting another.

The ratio of the length of the side opposite an acute angle in a right triangle to the side adjacent to the angle. The tangent of an angle is equal to the sine of the angle divided by the cosine of the angle.

The ratio of the ordinate to 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 tangent of an angle whose measure in radians is equal to x.