(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).

Origin of sine

1585–95; < New Latin,Latinsinus a curve, fold, pocket, translation of Arabicjayb literally, pocket, by folk etymology < Sanskritjiyā, jyā chord of an arc, literally, bowstring

nil sine numine

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

Latin.

nothing without the divine will: motto of Colorado.

sine qua non

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

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

causa sine qua non

[kou-sah si-ne kwah nohn; Englishkaw-zuhsahy-nee kwey non, kaw-zuhsin-ey kwah nohn]

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

Abbreviation: sin

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

sine

^{2}

preposition

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

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.

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 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.”

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.