# 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^{}

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

## Examples from the Web for cosine

### Historical Examples

#### 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

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

### n.

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.