# cosine

[koh-sahyn]

- Trigonometry.
- (in a right triangle) the ratio of the side adjacent to a given angle to the hypotenuse.
- the sine of the complement of a given angle or arc. Abbreviation: cos

- Mathematics. (of a real or complex number x) the function cos x defined by the infinite series 1 − (x2/2!) + (x4/4!) − + …, where ! denotes factorial. Abbreviation: cosCompare sine(def 3), factorial(def 1).

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## Origin of cosine

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

## Examples from the Web for cosine

### Historical Examples of cosine

Like the functions sine and cosine, the elliptic functions have addition theorems, e.g.

The New Gresham EncyclopediaVarious

And, seating himself beside Dirrik, he began to explain the mysteries of sine, cosine and tangent.

Dry Fish and WetAnthon Bernhard Elias Nilsen

These are then respectively the sine and cosine of the angle α between the radius and one of the axes (O X).

The inventions, researches and writings of Nikola TeslaThomas Commerford Martin

Multiply this by the cosine of the angle and divide by the sine, and we shall get the value of the arc QY for the equator.

Outlines of a Mechanical Theory of StormsT. Bassnett

Nevertheless, I bear no grudge against the sine and the cosine, which I continue to hold in high esteem.

The Life of the FlyJ. Henri Fabre

## cosine

- a trigonometric function that in a right-angled triangle is the ratio of the length of the adjacent side to that of the hypotenuse; the sine of the complementAbbreviation: cos

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## Word Origin for cosine

C17: from New Latin cosinus; see co-, sine 1

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 cosine

1630s, from co. sinus, abbreviation of Medieval Latin complementi sinus (see complement + sine).

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Online Etymology Dictionary, © 2010 Douglas Harper

## cosine

[kō′sīn′]

- The ratio of the length of the side adjacent to an acute angle of a right triangle to the length of the hypotenuse.
- 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 cosine 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.