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sine

[sahyn] /saɪn/
noun
1.
Trigonometry.
  1. (in a right triangle) the ratio of the side opposite a given acute angle to the hypotenuse.
  2. (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.
2.
Geometry. (originally) a perpendicular line drawn from one extremity of an arc of a circle to the diameter that passes through its other extremity.
3.
Mathematics. (of a real or complex number x) the function sin x defined by the infinite series x − (x 3 /3!) + (x 5 /5!) − + …, where ! denotes factorial.
Compare cosine (def 2), factorial (def 1).
Origin of sine
1585-1595
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

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.
1.
nothing without the divine will: motto of Colorado.

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
1.
an indispensable condition, element, or factor; something essential:
Her presence was the sine qua non of every social event.
Origin
From the Late Latin word sine quā (causā) nōn without which (thing) not

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.
1.
an indispensable condition; requisite.
Origin
literally, a cause without which not
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2017.
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British Dictionary definitions for sine

sine1

/saɪn/
noun (of an angle)
1.
  1. a trigonometric function that in a right-angled triangle is the ratio of the length of the opposite side to that of the hypotenuse
  2. 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
sin
Word Origin
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

sine2

/ˈsaɪnɪ/
preposition
1.
(esp in Latin phrases or legal terms) lacking; without

sine qua non

/ˈsaɪnɪ kweɪ ˈnɒn/
noun
1.
an essential condition or requirement
Word Origin
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
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Word Origin and History for sine
n.

trigonometric function, 1590s (in Thomas Fale's "Horologiographia, the Art of Dialling"), from Latin sinus "fold in a garment, bend, curve, bosom" (see sinus). Used mid-12c. by Gherardo of Cremona in Medieval Latin translation of Arabic geometrical text to render Arabic jiba "chord of an arc, sine" (from Sanskrit jya "bowstring"), which he confused with jaib "bundle, bosom, fold in a garment."

sine qua non

"an indispensable condition," Latin, literally "without which not," from sine "without" (see sans) + qua ablative fem. singular of qui "which" (see who) + non "not" (see non-). Feminine to agree with implied causa. The Latin phrase is common in Scholastic use. Sometimes a masculine form, sine quo non, is used when a person is intended. Proper plural is sine quibus non.

Online Etymology Dictionary, © 2010 Douglas Harper
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sine in Science
sine
  (sīn)   
  1. The ratio of the length of the side opposite an acute angle in a right triangle to the length of the hypotenuse.

  2. 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.

  3. 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 © 2002. Published by Houghton Mifflin. All rights reserved.
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sine in Culture
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 American Heritage® New Dictionary of Cultural Literacy, Third Edition
Copyright © 2005 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.
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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 Company. Published by Houghton Mifflin Company.
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