• synonyms


[koh-tan-juh nt, koh-tan-]
noun Trigonometry.
  1. (in a right triangle) the ratio of the side adjacent to a given angle to the side opposite.
  2. the tangent of the complement, or the reciprocal of the tangent, of a given angle or arc. Abbreviation: cot, ctn
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Also co·tan [koh-tan] /ˈkoʊˌtæn/.

Origin of cotangent

First recorded in 1625–35, cotangent is from the New Latin word cotangent- (stem of cotangēns). See co-, tangent
Related formsco·tan·gen·tial [koh-tan-jen-shuh l] /ˌkoʊ tænˈdʒɛn ʃəl/, adjective
Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018

British Dictionary definitions for cotangent


  1. (of an angle) a trigonometric function that in a right-angled triangle is the ratio of the length of the adjacent side to that of the opposite side; the reciprocal of tangentAbbreviation: cot, cotan, ctn
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Derived Formscotangential (ˌkəʊtænˈdʒɛnʃəl), adjective
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

Word Origin and History for cotangent


from co. tangent, abbreviation of complement + tangent.

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Online Etymology Dictionary, © 2010 Douglas Harper

cotangent in Science


  1. The ratio of the length of the adjacent side of an acute angle in a right triangle to the length of the opposite side. The cotangent is the inverse of the tangent.
  2. 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.
  3. A function of a number x, equal to the cotangent of an angle whose measure in radians is equal to x.
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The American Heritage® Science Dictionary Copyright © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.