tangent

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tangent in mathematics. 1 In geometry, the tangent to a circle or sphere is a straight line that intersects the circle or sphere in one and only one point. For other curves and surfaces the tangent line at a given point P is defined as the limiting position, if such a limit exists, of a secant line through P and another point P′ on the curve or surface as P′ is allowed to approach P. The tangent plane to a surface at a point is the plane in which every line in the plane that passes through the point is a tangent line to the surface at that point. The study of tangent lines and planes usually requires the concepts of the calculus and is included within the scope of differential geometry . 2 A trigonometric function. See trigonometry .

tan·gent / ˈtanjənt/ • n. 1. a straight line or plane that touches a curve or curved surface at a point, but if extended does not cross it at that point. ∎ fig. a completely different line of thought or action: she went off on a tangent about how she and her husband had driven past a department store window. 2. Math. the trigonometric function that is equal to the ratio of the sides (other than the hypotenuse) opposite and adjacent to an angle in a right triangle. • adj. (of a line or plane) touching, but not intersecting, a curve or curved surface. DERIVATIVES: tan·gen·cy / -jənsē/ n.

tangent

tangent (from Lat. tangere, to touch). Part of clavichord, a small metal ‘tongue’, which touches a str. when key is struck and produces sound. Remains in contact with str. while note sounds.

tangent In trigonometry, ratio of the length of the side opposite an acute angle to the length of the side adjacent to it within a right-angle triangle.

tangent (geom.) adj. touching at a point XVI; sb. XVI. — L. tangēns, -ent-, prp. of tangere touch. See -ENT.
Hence tangential XVII.

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