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
Six hundred years ago, mathematicians were building tables of sines and cosines, which were needed for navigation, but these can now be generated by computers in seconds.
—
Matteo Wong, The Atlantic, 4 Oct. 2024
For the mathematically curious, x = cosine (2π ⁄17).
—Jack Murtagh, Scientific American, 12 Sep. 2024
As Laplace had suggested in 1775, each tidal constituent can be represented as a repeating cosine curve, but those curves are specific to a location and can be calculated only through the collection of tidal data.
—IEEE Spectrum, 2 June 2024
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
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Matteo Wong, The Atlantic, 4 Oct. 2024
For the mathematically curious, x = cosine (2π ⁄17).
—Jack Murtagh, Scientific American, 12 Sep. 2024
As Laplace had suggested in 1775, each tidal constituent can be represented as a repeating cosine curve, but those curves are specific to a location and can be calculated only through the collection of tidal data.
—IEEE Spectrum, 2 June 2024
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
Cite this Entry
“Cosine.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/cosine. Accessed 5 Mar. 2025.
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cosine
noun
co·sine
ˈkō-ˌsīn 
: a trigonometric function that is the ratio between the side next to an acute angle in a right triangle and the hypotenuse
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