sine

Definitions

• WordNet 3.6
• n sine ratio of the length of the side opposite the given angle to the length of the hypotenuse of a right-angled triangle
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Webster's Revised Unabridged Dictionary
• n Sine (Trig) The length of a perpendicular drawn from one extremity of an arc of a circle to the diameter drawn through the other extremity.
• prep Sine Without.
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Century Dictionary and Cyclopedia
• sine After that; afterward: same as since, 1.
• sine Before now; ago: same as since, 3: as, lang syne, long ago, used also as a noun, especially in the phrase auld langsyne, old times (see langsyne).
• sine After; since: same as since.
• n sine A gulf.
• n sine In trigonometry, formerly, with reference to any arc of a circle, the line drawn from one extremity of the arc at right angles to the diameter which passes through its other extremity; now ordinarily, with reference not to the arc but to the angle which it subtends at the center of the circle, the ratio of the aforesaid line to the radius of the circle. Thus, in the diagram, BE is the sine of the arc AB (sometimes it is defined as half the chord of double the arc), and the ratio of BE to CE is the sine of the angle ACB. (See trigonometrical functions, under trigonometrical.) A more scientific definition of the sine is that of Euler, sin x =½ i (e—xi—e), where i =—1, and e is the Napierian base. The sine is also fully defined by the infinite series But all the properties of sines are readily deduced from the definition that the sine is such a function that it vanishes with the variable, while Abbreviated sin, as in formulæ here given.
• n sine the function expressed by the series These functions were invented by Wronski.
• sine To strain.
• sine To leave off milking a cow.
• sine A Latin preposition, signifying ‘without.’ See sine die, sine qua non.
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Chambers's Twentieth Century Dictionary
• n Sine sīn a straight line drawn from one extremity of an arc perpendicular to the diameter that passes through the other extremity.
• adv Sine sīn (Scot.) after that: ago
• conj Sine since
• prep Sine sī′ne without, as in Sine die, without day, of an adjournment; Sine quâ non, an indispensable condition, &c.
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Quotations

• Janet Malcolm
“Fidelity to the subject's thought and to his characteristic way of expressing himself is the sine qua non of journalistic quotation.”

Etymology

Webster's Revised Unabridged Dictionary
LL. sinus, a sine, L. sinus, bosom, used in translating the Ar. jaib, properly, bosom, but probably read by mistake (the consonants being the same) for an original jība, sine, from Skr. jīva, bowstring, chord of an arc, sine
Chambers's Twentieth Century Dictionary
L.

Usage

In literature:

Haec tum nomina erunt, nunc sunt sine nomine terrae.
"The Spectator, Volumes 1, 2 and 3" by Joseph Addison and Richard Steele
Dignare, Dulcis Maria, mine et semper nos sine delicto conservare.
"Primitive Christian Worship" by James Endell Tyler
Ergo et legibus et institutis vacat aetas nostra muneribus eis quae non possunt sine viribus sustineri.
"Cato Maior de Senectute" by Marcus Tullius Cicero
Medetur lienibus ... Narrantque sues qui radicem ejus ederint sine splene inveniri.
"Notes and Queries, Number 55, November 16, 1850" by Various
In Alemtejo, south of Cape de Sines, are several of these, usually about 6 feet in length, with a slight portico at one end.
"Rough Stone Monuments and Their Builders" by T. Eric Peet
Also when it comes it won't certainly come 'sine te.
"The Letters of Robert Browning and Elizabeth Barrett Barrett, Vol. 1 (of 2) 1845-1846" by Robert Browning and Elizabeth Barrett Barrett
Spring's Glory, Vindicating Love by Temperance, against the Tenet, Sine Cerere & Baccho friget Venus; moralized in a Masque.
"The Lives of the Poets of Great Britain and Ireland (1753)" by Theophilus Cibber
Sine ejus consilio nullus ordinetur.
"Observations upon the Prophecies of Daniel, and the Apocalypse of St. John" by Isaac Newton
Davey Sine the eldest brother, went to reside at Bhanpoor, in the neighbourhood.
"A Journey through the Kingdom of Oude, Volumes I & II" by William Sleeman
Toletus in summa casuum conscientiae, sine instructione sacerdotum li.
"A Treatise of Witchcraft" by Alexander Roberts
Lockley interpreted the term to mean sine waves, rounded at top and trough.
"Operation Terror" by William Fitzgerald Jenkins
Uncle Jimmie leaves a sine on the door when he goes out.
"Turn About Eleanor" by Ethel M. Kelley
Principal, Prof. E. C. Sine; Teachers, Miss Fannie Weadon, Miss Ruth Dyer, Miss Ida N. Ball.
"A Virginia Village" by Charles A. Stewart
Et capit amerciamenta pistorum et braciatorum et hoc sine waranto ut credimus.
"Notes and Queries, Number 84, June 7, 1851" by Various
Non dolet hic, quisquis landari, Gellia, quaerit; Ille dolet vere, qui sine teste dolet.
"Dealings with the Dead, Volume I (of 2)" by A Sexton of the Old School
Excolui juvenum ingenia, et praecepta Minervae Tradens consenui, cathedraeque piget sine fructu.
"The Dance of Death" by Francis Douce
Quartus fuit Robertus Stot qui eciam mortuus est sine herede.
"Villainage in England" by Paul Vinogradoff
He was the first to make use of sines instead of chords, and versed sines.
"Astronomical Curiosities" by J. Ellard Gore
That the landdrost has caused to be written on the gates of Kroonstad, "Nil sine Laboere"?
"War's Brighter Side" by Julian Ralph
Under perfect conditions of symmetry, the intensity of effect is found to vary as the sine of the directive angle.
"Life Movements in Plants, Volume II, 1919" by Sir Jagadis Chunder Bose
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In poetry:

I doubt if King John
Was a sine qua non.
I could rather imagine it
Of any other Plantagenet.
"Clerihew - King John" by Edmund Clerihew Bentley

In news:

The new line of UPS systems from Middle Atlantic features Pure Sine Wave technology, integration with AV control systems, and a sliding rackrail mount for single-person UPS mounting capability.
Kyle Nathaniel Sine - France, infant son of Joseph France and Valery Sine -France, passed away Wednesday, Nov 7, 2012.
In addition to his parents, he is survived by a sister, Michele Sine .
Humboldt Bay tides follow sine curves.
The oddly titled Sine Mora is a throwback to perhaps the most hardcore of genres, the sidescrolling shooter.
The 40th day of the session is called sine die.
SINE DIE – Thursday, April 14, 2011.
GOVERNOR O'MALLEY, SENATE PRESIDENT MILLER, SPEAKER BUSCH HOLD FIRST BILL SIGNING FOLLOWING 2011 SINE DIE.
Trisha and Kelly Sine of Paden City announce the engagement of their daughter, Miranda Sine , to Brandon Corcoran of Paden City, son of Mary and Ted Pearson and Rick and Dana Corcoran.
Trisha and Kelly Sine of Paden City announce the engagement of their daughter, Miranda Sine , to Brandon Corcoran of Paden City, son of Mary and Ted Pearson and Rick and Dana Corcora.
Legislators still looking for budget agreement despite blooms on the sine die tree.
The first session of the 111th Congress is now over, as the House and Senate have adjourned sine die for the year.
The Kidston Pavilion at Fellows Riverside Gardens in Youngstown was the setting on July 24 for the summer wedding of Mark S Kellerman Jr and his bride, Jennifer L Sine .
GOVERNOR O'MALLEY, SENATE PRESIDENT MILLER, SPEAKER BUSCH HOLD FIRST BILL SIGNING FOLLOWING 2011 SINE DIE .
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In science:

In [CL] Costin and Lebowitz proved the Central Limit Theorem for #[−L,L] in the case of the sine kernel.
Determinantal random point fields
Hence we obtain a determinantal random point process given by the sine kernel, .
Non-intersecting Paths, Random Tilings and Random Matrices
We want to show that this is a determinantal point process, , given by the discrete sine kernel.
Non-intersecting Paths, Random Tilings and Random Matrices
In this scaling limit we will obtain the sine kernel determinantal point process of random matrix theory.
Non-intersecting Paths, Random Tilings and Random Matrices
In order to compare these operators to our approach we shall use the deﬁnition of Carruthers and Nieto for the Hermitian sine S ≡ 1 2i (E − E† ) and cosine C ≡ 1 2 (E + E†) operators.
The quantum phase problem: steps toward a resolution
In order to compare |S| with the sine of Φ, it is enough to ﬁnd the relation between the square of these operators.
The quantum phase problem: steps toward a resolution
Cross-correlation (A), RR (B), DET (C) and L (D) for two delayed sine functions. L has the unit of time.
Nonlinear analysis of bivariate data with cross recurrence plots
These particular excitations are solutions of the sine-Gordon equation, which, in the wide ﬁeld of the NLE, is to be considered as a prototype model .
Elementary Excitations in Quantum Antiferromagnetic Chains: Dyons, Spinons and Breathers
In low ﬁeld, the agreement with the sine-Gordon model (the full line) is very good: EG = emJ ≃ H 2/3 .
Elementary Excitations in Quantum Antiferromagnetic Chains: Dyons, Spinons and Breathers
We need large values of k in order to increase the effective domain of the sine function.
A mechanism for randomness
In the spherically symmetric case a relation has been established with solutions of the Sine-Gordon and the λφ4 equations .
Static charged perfect fluid spheres in general relativity
Other choices lead to two-dimensional integrable models, like the sine-Gordon equation .
Static charged perfect fluid spheres in general relativity
On the other hand, for the same reason the corrections of the coeﬃcients of the ﬁrst and third cosine and sine terms are small.
The effects of blending on the light curve shape of Cepheids
The bosonization of the Luttinger liquid model leads to the quantum sine-Gordon model (eq.(1.45)) which is an integrable system and has extensively been studied as a prototype nonlinear quantum (or classical) ﬁeld theory.
Transport in one dimensional quantum systems
We should also mention that a similar analysis for lattice regularization of the sine-Gordon model (periodic X X Z chain in transverse magnetic ﬁeld) also gave results consistent with the DHN formula .
Reply to ``Comment on `Properties of the massive Thirring model from the XYZ spin chain' "
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