/tan"jeuhnt/, adj.1. in immediate physical contact; touching.2. Geom.a. touching at a single point, as a tangent in relation to a curve or surface.b. in contact along a single line or element, as a plane with a cylinder.3. tangential (def. 3).n.4. Geom. 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. Trig.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. Abbr.: tg, tgnc. (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.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.[1585-90; < L tangent- (s. of tangens, prp. of tangere to touch) in phrase linea tangens touching line; see -ENT]Syn. 1. meeting, abutting.
* * *▪ of a curvein geometry, straight line (or smooth curve) that touches a given curve at one point; at that point the slope of the curve is equal to that of the tangent. A tangent line may be considered the limiting position of a secant line as the two points at which it crosses the curve approach one another. Tangent planes and other surfaces are defined analogously. (See Figure—>.)The trigonometric law of tangents is a relationship between two sides of a plane triangle and the tangents of the sum and difference of the angles opposite those sides. In any plane triangle ABC, if a, b, and c are the sides opposite angles A, B, and C, respectively, thenThe formula is especially useful in making calculations using logarithms.In trigonometry of a right triangle, the tangent of an angle is the ratio of the side opposite the angle to the side adjacent. The value of the tangent (ratio) depends only on the size of the angle, not on the particular right triangle used to compute it.
* * *