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.
5.
Trigonometry.
a.
(in a right triangle) the ratio of the side opposite a given angle to the side adjacent to the angle.
b.
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
c.
(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.
6.
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.
—Idiom
7.
off on or at a tangent, digressing suddenly from one course of action or thought and turning to another: The speaker flew off on a tangent.
Origin: 1585–90; < L tangent- (s. of tangēns, prp. of tangere to touch) in phrase līnea tangēns touching line; see -ent