# sine

## noun

1
: the trigonometric function that for an acute angle is the ratio between the leg opposite the angle when it is considered part of a right triangle and the hypotenuse
2
: a trigonometric function sin θ that for all real numbers θ is exactly equal to the sine of an angle of measure θ in radians and that is given by the sum of the alternating series {latex}\sin \theta = \theta - \frac{\theta^{3}}{3!} + \frac{\theta^{5}}{5!} - \frac{\theta^{7}}{7!} + \frac{\theta^{9}}{9!} - \dots{/latex}

## Examples of sine in a Sentence

Recent Examples on the Web Automorphic forms are a generalization of periodic functions like the sine in trigonometry, whose outputs endlessly repeat as inputs grow. Kevin Hartnett, Quanta Magazine, 12 Oct. 2023 These functions, such as the sine and cosine, are defined using right triangles. Leila Sloman, Scientific American, 10 Apr. 2023 Mathematicians define the sine of this angle as the height of the vertical side divided by the length of the hypotenuse. 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 That would be the strongest annual gain sine 1951. Arkansas Online, 28 May 2021 The answer: nothing. Remember that the basic trig functions (sine, cosine, tangent) are just ratios of sides of right triangles. Rhett Allain, Wired, 14 Mar. 2022 In 1807, Joseph Fourier discovered that any periodic function — an equation whose values repeat cyclically — could be expressed as the sum of trigonometric functions like sine and cosine. Quanta Magazine, 13 Oct. 2021 This geometric structure is closely connected to important ideas in trigonometry, like the angle sum and difference formulas for sine and cosine, the theory of rotations of the plane, and e, the base of the natural logarithm function. Quanta Magazine, 23 Sep. 2021

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'sine.' 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

Medieval Latin sinus, from Latin, curve

First Known Use

1593, in the meaning defined at sense 1

Time Traveler
The first known use of sine was in 1593

sine

## Cite this Entry

“Sine.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/sine. Accessed 13 Apr. 2024.

## Kids Definition

sine

noun
: a trigonometric function that for an acute angle in a right triangle is the ratio of the side opposite the angle to the hypotenuse

## More from Merriam-Webster on sine

Love words? Need even more definitions?

Subscribe to America's largest dictionary and get thousands more definitions and advanced search—ad free!