tangent line


tangent line
In geometry, a line that intersects a circle exactly once; in calculus, a line that touches a curve at one point and whose slope is equal to that of the curve at that point.

Particularly useful as approximations of curves in the immediate vicinity of the point of tangency, tangent lines are the basis of many estimation techniques, including linear approximation. The numerical value of the slope of the tangent line to the graph of a function at any point equals that of the function's derivative at that point. This is one of the keystones of differential calculus. See also differential geometry.

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Universalium. 2010.

Look at other dictionaries:

  • tangent line — noun Etymology: translation of New Latin linea tangens : a line at a fixed point P of a curve that is the limit approached by the secant PQ as Q approaches P along the curve …   Useful english dictionary

  • Tangent — Tan gent, n. [L. tangens, entis, p. pr. of tangere to touch; akin to Gr. ? having seized: cf. F. tangente. Cf. {Attain}, {Contaminate}, {Contingent}, {Entire}, {Tact}, {Taste}, {Tax}, v. t.] (Geom.) A tangent line curve, or surface; specifically …   The Collaborative International Dictionary of English

  • Tangent galvanometer — Tangent Tan gent, n. [L. tangens, entis, p. pr. of tangere to touch; akin to Gr. ? having seized: cf. F. tangente. Cf. {Attain}, {Contaminate}, {Contingent}, {Entire}, {Tact}, {Taste}, {Tax}, v. t.] (Geom.) A tangent line curve, or surface;… …   The Collaborative International Dictionary of English

  • Tangent of an angle — Tangent Tan gent, n. [L. tangens, entis, p. pr. of tangere to touch; akin to Gr. ? having seized: cf. F. tangente. Cf. {Attain}, {Contaminate}, {Contingent}, {Entire}, {Tact}, {Taste}, {Tax}, v. t.] (Geom.) A tangent line curve, or surface;… …   The Collaborative International Dictionary of English

  • Tangent of an arc — Tangent Tan gent, n. [L. tangens, entis, p. pr. of tangere to touch; akin to Gr. ? having seized: cf. F. tangente. Cf. {Attain}, {Contaminate}, {Contingent}, {Entire}, {Tact}, {Taste}, {Tax}, v. t.] (Geom.) A tangent line curve, or surface;… …   The Collaborative International Dictionary of English

  • tangent — [tan′jənt] adj. [L tangens, prp. of tangere, to touch: see TACT] 1. that touches; touching 2. Geom. touching and not intersecting a curve or curved surface at one and only one point: said of a line or plane n. [< ModL ( linea) tangens, tangent …   English World dictionary

  • Tangent lines to circles — In Euclidean plane geometry, tangent lines to circles form the subject of several theorems, and play an important role in many geometrical constructions and proofs. Since the tangent line to a circle at a point P is perpendicular to the radius to …   Wikipedia

  • Tangent — For the tangent function see trigonometric functions. For other uses, see tangent (disambiguation). In geometry, the tangent line (or simply the tangent) to a curve at a given point is the straight line that just touches the curve at that point… …   Wikipedia

  • tangent — /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.… …   Universalium

  • tangent — I. adjective Etymology: Latin tangent , tangens, present participle of tangere to touch; perhaps akin to Old English thaccian to touch gently, stroke Date: 1594 1. a. meeting a curve or surface in a single point if a sufficiently small interval… …   New Collegiate Dictionary


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