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off at a tangent

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tan⋅gent

  [tan-juhnt]
Use off at a tangent in a Sentence
–adjective
1. in immediate physical contact; touching.
2. Geometry.
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).
–noun
4. 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

Synonyms:
1. meeting, abutting.
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2009.
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Word Origin & History

tangent  (adj.)
1594, "meeting at a point without intersecting," from L. tangentem (nom. tangens), prp. of tangere "to touch," from PIE base *tag- "to touch, to handle" (cf. L. tactus "touch," Gk. tetagon "having seized," O.E. þaccian "stroke, strike gently"). First used by Dan. mathematician Thomas Fincke in "Geomietria Rotundi" (1583). The noun also is attested from 1594; extended sense of "slightly connected with a subject" is first recorded 1825. Tangential is recorded from 1630; fig. sense of "divergent, erratic" is from 1787.
Online Etymology Dictionary, © 2001 Douglas Harper
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Science Dictionary
tangent   (tān'jənt)  Pronunciation Key 

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

  2. 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.

  3. 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.

  4. A function of a number x, equal to the tangent of an angle whose measure in radians is equal to x.


The American Heritage® Science Dictionary
Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
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