# sine

[ sahyn ]

/ saɪn /

### noun

Trigonometry.

- (in a right triangle) the ratio of the side opposite a given acute angle to the hypotenuse.
- (of an angle) a trigonometric function equal to the ratio of the ordinate of the end point of the arc to the radius vector of this end point, the origin being at the center of the circle on which the arc lies and the initial point of the arc being on the x-axis. Abbreviation: sin

Geometry. (originally) a perpendicular line drawn from one extremity of an arc of a circle to the diameter that passes through its other extremity.

Mathematics. (of a real or complex number x) the function sin x defined by the infinite series x − (x3/3!) + (x5/5!) − + …, where ! denotes factorial.Compare cosine(def 2), factorial(def 1).

## Words nearby sine

## Origin of sine

1585–95; < New Latin, Latin sinus a curve, fold, pocket, translation of Arabic jayb literally, pocket, by folk etymology < Sanskrit jiyā, jyā chord of an arc, literally, bowstring

## Definition for sine (2 of 4)

nil sine numine

[ neel sin-e noo-mi-ne; English nil sin-ee noo-mi-nee, nyoo- ]

/ nil ˈsɪn ɛ ˈnu mɪ nɛ; English nɪl ˈsɪn i ˈnu mɪ ni, ˈnyu- /

### Latin.

nothing without the divine will: motto of Colorado.

## Definition for sine (3 of 4)

sine qua non

[ sahy-nee kwey non, kwah, sin-ey; Latin si-ne kwah-nohn ]

/ ˈsaɪ ni kweɪ ˈnɒn, kwɑ, ˈsɪn eɪ; Latin ˈsɪ nɛ kwɑˈnoʊn /

### noun

an indispensable condition, element, or factor; something essential: Her presence was the sine qua non of every social event.

## Origin of sine qua non

From the Late Latin word sine quā (causā) nōn without which (thing) not

## Definition for sine (4 of 4)

causa sine qua non

[ kou-sah si-ne kwah nohn; English kaw-zuh sahy-nee kwey non, kaw-zuh sin-ey kwah nohn ]

/ ˈkaʊ sɑ ˈsɪ nɛ kwɑ ˈnoʊn; English ˈkɔ zə ˈsaɪ ni kweɪ ˈnɒn, ˈkɔ zə ˈsɪn eɪ kwɑ ˈnoʊn /

### noun Latin.

an indispensable condition; requisite.

## Origin of causa sine qua non

literally, a cause without which not

Dictionary.com Unabridged
Based on the Random House Unabridged Dictionary, © Random House, Inc. 2020

## Examples from the Web for sine

## British Dictionary definitions for sine (1 of 3)

sine

^{1}/ (saɪn) /

### noun (of an angle)

- a trigonometric function that in a right-angled triangle is the ratio of the length of the opposite side to that of the hypotenuse
- a function that in a circle centred at the origin of a Cartesian coordinate system is the ratio of the ordinate of a point on the circumference to the radius of the circle

## Word Origin for sine

C16: from Latin sinus a bend; in New Latin, sinus was mistaken as a translation of Arabic jiba sine (from Sanskrit jīva, literally: bowstring) because of confusion with Arabic jaib curve

## British Dictionary definitions for sine (2 of 3)

sine

^{2}/ (ˈsaɪnɪ) /

### preposition

(esp in Latin phrases or legal terms) lacking; without

## British Dictionary definitions for sine (3 of 3)

sine qua non

/ Latin (ˈsaɪnɪ kweɪ ˈnɒn) /

### noun

an essential condition or requirement

## Word Origin for sine qua non

literally: without which not

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

## Scientific definitions for sine

sine

[ sīn ]

The ratio of the length of the side opposite an acute angle in a right triangle to the length of the hypotenuse.

The ordinate 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 sine of an angle whose measure in radians is equal to x.

The American Heritage® Science Dictionary
Copyright © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

## Cultural definitions for sine

sine qua non

[ (sin-i kwah non, nohn) ]

The essential, crucial, or indispensable ingredient without which something would be impossible: “Her leadership was the sine qua non of the organization's success.” From Latin, meaning “without which nothing.”

The New Dictionary of Cultural Literacy, Third Edition
Copyright © 2005 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

## Idioms and Phrases with sine

sine qua non

An essential element or condition, as in A perfect cake is the since qua non of a birthday party. This phrase is Latin for “without which not” and has been used in English since about 1600. It appears more in writing than in speech.

The American Heritage® Idioms Dictionary
Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.