# cosine

## noun

co·​sine
1
: a trigonometric function that for an acute angle is the ratio between the leg adjacent to the angle when it is considered part of a right triangle and the hypotenuse
2
: a trigonometric function cos θ that for all real numbers θ is given by the sum of the alternating series {latex}1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!} + \frac{x^8}{8!} - \dots{/latex} and that is exactly equal to the cosine of an angle of measure θ in radians

## Examples of cosine in a Sentence

Recent Examples on the Web Just as the values of the cosine function repeat in intervals of 2π, a modular form is periodic in one-unit intervals. Jordana Cepelewicz, Quanta Magazine, 21 Sep. 2023 By rounding off the squared cosine function (through the square brackets), f(x) returns the value 1 as desired if x is a prime and 0 otherwise. Manon Bischoff, Scientific American, 16 Nov. 2023 The Million Dollars Remains Unclaimed Wilson’s theorem can be used to build a detector: the cosine of an integer multiple of π always yields 1 or -1, while all other arguments of the cosine function, on the other hand, yield a result smaller than 1. Manon Bischoff, Scientific American, 16 Nov. 2023 This additional symmetry makes functions like cosine incredibly useful. Jordana Cepelewicz, Quanta Magazine, 21 Sep. 2023 The cosine of this angle is the length of the horizontal side divided by the hypotenuse. Leila Sloman, Scientific American, 10 Apr. 2023 These functions, such as the sine and cosine, are defined using right triangles. Leila Sloman, Scientific American, 10 Apr. 2023 Although the proof is an impressive bit of mathematics, other mathematicians have employed similar approaches before, using sine and cosine to independently prove the Pythagorean Theorem without relying on sin²α + cos²α = 1. Darren Orf, Popular Mechanics, 31 Mar. 2023 Illustration: Rhett Allain This solution includes the trigonometric function cosine. Rhett Allain, WIRED, 14 Mar. 2023

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'cosine.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

## Word History

Etymology

New Latin cosinus, from co- + Medieval Latin sinus sine

First Known Use

1635, in the meaning defined at sense 1

Time Traveler
The first known use of cosine was in 1635

cosine

## Cite this Entry

“Cosine.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/cosine. Accessed 12 Apr. 2024.

## Kids Definition

cosine

noun
co·​sine
: a trigonometric function that is the ratio between the side next to an acute angle in a right triangle and the hypotenuse

## More from Merriam-Webster on cosine

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