# cotangent

[koh-tan-juh nt, koh-tan-]

- (in a right triangle) the ratio of the side adjacent to a given angle to the side opposite.
- 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^{}

Dictionary.com Unabridged
Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018

## cotangent

- (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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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

### n.

from co. tangent, abbreviation of complement + tangent.

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Online Etymology Dictionary, © 2010 Douglas Harper

## cotangent

[kō-tăn′jənt]

- 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.
- 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.
- 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.