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# cosine

[ **koh**-sahyn ]

## noun

*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. : cos

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

cosine

/ ˈkəʊˌsaɪn /

## noun

- 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 complement cos

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.*

## Word History and Origins

Origin of cosine^{1}

## Word History and Origins

Origin of cosine^{1}

*cosinus;*see co- , sine

^{1}

## Example Sentences

Thanks to the exponent on the cosine function, this function does some strange things when N is less than 1.

The variables do not literally represent the angle measurements themselves, but instead stand in for complex numbers associated to the cosines of the angles.

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

The sine and the cosine I shall have occasion to employ in the latter part of my lecture.

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

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

The nine cosine-inclinations above are, as has been seen, connected by six equations.

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