Tangent Point Line Curve Angle Equal Straight B

tan·gent

I

\\ˈtan-jənt\\ adjective1.
  a. meeting a curve or surface in a single point if a sufficiently small interval is considered
      straight line tangent to a curve
  b.
    (1) having a common tangent line at a point
       tangent curves
    (2) having a common tangent plane at a point
       tangent surfaces
2. diverging from an original purpose or course :

irrelevant

    tangent remarks

II

noun1.
  a. the trigonometric function that for an acute angle is the ratio between the leg opposite to the angle when it is considered part of a right triangle and the leg adjacent
  b. a trigonometric function that is equal to the sine divided by the cosine for all real numbers θ for which the cosine is not equal to zero and is exactly equal to the tangent of an angle of measure θ in radians
2. a line that is tangent; specifically : a straight line that is the limiting position of a secant of a curve through a fixed point and a variable point on the curve as the variable point approaches the fixed point
3. an abrupt change of course :

digression

    the speaker went off on a tangent
4. a small upright flat-ended metal pin at the inner end of a clavichord key that strikes the string to produce the tone

tangent
  tangent (adj.)
  1590s, "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 1590s; extended sense of "slightly connected with a subject" is first recorded 1825.

tangent
tan·gent / 5tAndVEnt / noun1. (geometry 几何) a straight line that touches the outside of a curve but does not cross it
   切线
2. (abbr. tan) (mathematics 数) the

ratio

of the length of the side opposite an angle in a

right-angled

triangle to the length of the side next to it
   正切
⇨ compare

cosine

,

sine

 IDIOMS 
▪ fly / go off at a 'tangent
(BrE) (NAmE go off on a 'tangent) (informal)
   to suddenly start saying or doing sth that does not seem to be connected to what has gone before
   突然转换话题；突然改变行动

tan·gent
I. \ˈtanjənt, ˈtaan-\ adjective
Etymology: Latin tangent-, tangens, present participle of tangere to touch; akin to Greek tetagōn having seized, Old English thaccian to stroke, touch gently
1.
 a. : touching at a single point
  < a straight line tangent to a curve >
 b.
  (1) : having a common tangent line at a point — used of two curves in a plane, two space curves, or a surface and a space curve
  (2) : having a common tangent plane at a point — used of two surfaces
2.
 a. : diverging from an original purpose or course :
  < much of his work is chaotic and distorted by tangent obsessions — Tennessee Williams >
 b. : : being in agreement
  < subject matter tangent to the country's growth in those years — M.F.Milton >
II. noun
(-s)
Etymology: New Latin tangent-, tangens, from Latin, present participle of tangere to touch
1.
 a. :
 b. : the ordinate of any point on the terminal side of an angle divided by the nonzero abscissa of this point with the vertex coinciding with the origin of a plane rectangular coordinate system and the initial side of the angle coinciding with the positive x-axis — abbr. tan
2. : a course abruptly deviating from that previously pursued : ,
 < avoid wandering off on tangents — J.F.Wharton >
 < his critics … went off at a tangent — Saul Carson >
3. : a small upright flat-ended metal pin at the inner end of a clavichord key that strikes the string to produce the musical tone and fixes the pitch by damping the string
4. : a piece of straight railroad track
III. noun
: a trigonometric function that is equal to the sine divided by the cosine for all real numbers θ for which the cosine is not equal to zero and is exactly equal to the tangent of an angle of measure θ in radians

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