⁡ In programming languages, sin is typically either a built-in function or found within the language's standard math library. The CORDIC algorithm is commonly used in scientific calculators. ( f ( ⁡ C With modern CPU architectures this method may offer no advantage. 2 hypotenuse sin The leading term in the above equation, and the limit of arc length to distance ratio is given by: The law of sines states that for an arbitrary triangle with sides a, b, and c and angles opposite those sides A, B and C: This is equivalent to the equality of the first three expressions below: It can be proven by dividing the triangle into two right ones and using the above definition of sine. {\displaystyle \sin x} While the early study of trigonometry can be traced to antiquity, the trigonometric functions as they are in use today were developed in the medieval period. For example, computing modulo 1 or modulo 2 for a binary point scaled fixed-point value requires only a bit shift or bitwise AND operation. ) Sine definition at Dictionary.com, a free online dictionary with pronunciation, synonyms and translation. ◼ The x- and y-coordinates of this point of intersection are equal to cos(θ) and sin(θ), respectively. 7.640395578 ( 2 A table of some of these values is given below. Without the intention of returning. z For quotations using this term, see Citations:sine. y n ) . seine (plural seines) 1. {\textstyle \lim _{z\to 0}{\frac {\sin(\pi z)}{z}}=\pi } In mathematics, the sine is a trigonometric function of an angle. + z The arc length of the sine curve between {\displaystyle \mathbb {C} } For example, an angle sensor may count from 0 to 4096 over one complete revolution. This page was last edited on 26 December 2020, at 04:08. {\displaystyle \blacksquare }. 3. (pathology) An abnormal cavity or passage such as a fistula, caused by the destruction of tissue. Contextual translation of "sine pecunia" into English. yields, The function ( [9] With the exception of the sine (which was adopted from Indian mathematics), the other five modern trigonometric functions were discovered by Arabic mathematicians, including the cosine, tangent, cotangent, secant and cosecant. ( Use * for blank tiles (max 2) Advanced Search Advanced Search: Use * for blank spaces … can be decomposed as, Setting C 1 f π 4. 2048 π = . . ) sin It follows that the infinite product is holomorphic on The basic relationship between the sine and the cosine can also be expressed as the Pythagorean trigonometric identity:[2]. 1 Quell Learn more >> … {\displaystyle x} sinus (plural sinuses) 1. It follows that, Since and ln ) = Alle weiteren Informationen findest du im Haupteintrag sin. ⁡ e Using the unit circle definition has the advantage that the angle can be extended to any real argument. d With this restriction, for each x in the domain, the expression arcsin(x) will evaluate only to a single value, called its principal value. Initial mutations of a following adjective: Gregory Toner, Maire Ní Mhaonaigh, Sharon Arbuthnot, Dagmar Wodtko, Maire-Luise Theuerkauf, editors (2019) , “. 1 2 involves inaccuracies in representing 2 {\displaystyle z\in \mathbb {C} } 2. ∈ Hence, for some open and connected subset of In various branches of mathematics, the sine of an angle is determined in various ways, including the following: Apocope of English cinema, from French cinéma, shortening of cinématographe (term coined by the Lumière brothers in the 1890s), from the Ancient Greek κίνημα (kínēma, “movement”) + the French suffix -graphe. = 2 years ago. α Alternatively, the infinite product for the sine can be proved using complex Fourier series. From Old Irish sine (“teat, dug, pap”), from Proto-Celtic *sɸenyos, from Proto-Indo-European *pstḗn. cos ( For certain integral numbers x of degrees, the value of sin(x) is particularly simple. ⁡ ) From Proto-Celtic *sɸenyos, itself from Proto-Indo-European *pstḗn. ( ⁡ Learn sine in English translation and other related translations from Latin to English. can be written in closed form using special functions, but it is perhaps more instructive to write the decimal approximations of the Fourier coefficients. ∫ ⁡ The accuracy advantage stems from the ability to perfectly represent key angles like full-turn, half-turn, and quarter-turn losslessly in binary floating-point or fixed-point. 360 ( ) The parameter of each is a floating point value, specifying the angle in radians. Sine… NULLUS RECEDAT E CURIA CANCELLARIA SINE REMEDIO Latin, meaning No one should depart from a Court of Chancery without a remedy. absque, extra, citra, sed, set. Look it up now! cos ) 2 The sine of an acute angle is defined in the context of a right triangle: for the specified angle, it is the ratio of the length of the side that is opposite that angle, to the length of the longest side of the triangle (the hypotenuse). = ( Sine Die [Latin, Without day.] The arc length of the sine curve from 0 to x is the above number divided by The chord function was discovered by Hipparchus of Nicaea (180–125 BCE) and Ptolemy of Roman Egypt (90–165 CE). − From Old Irish sine, siniu, comparative form of sen (“old”). ( 0 By the identity theorem, the infinite product for the sine is valid for all n When only one value is desired, the function may be restricted to its principal branch. Others yet refer sine to Proto-Indo-European *seni (“for oneself, without”), itself maybe related to *swé or a locative of *senH. In Christian views it is an evil human act, which violates the rational nature of man as well as God's nature and his eternal law. {\textstyle {\frac {df}{dz}}={\frac {z}{z^{2}-n^{2}}}} The word sine defined here is the mathematical one, derived from the Latin "sinus." [9] Al-Khwārizmī (c. 780–850) produced tables of sines, cosines and tangents. [20]. {\displaystyle \ln(\sin(\pi z))+C_{0}} z 1 The definition of the sine function for complex arguments z: where i 2 = −1, and sinh is hyperbolic sine. This allows results to be looked up from a table rather than being calculated in real time. Introduction: In this article, Mary Harrell-Sesniak explains some of the old terms—many of them derived from Latin—that genealogists encounter during their family history research.Mary is a genealogist, author and editor with a strong technology background. sin Let a line through the origin intersect the unit circle, making an angle of θ with the positive half of the x-axis. , then the function The sine function is commonly used to model periodic phenomena such as sound and light waves, the position and velocity of harmonic oscillators, sunlight intensity and day length, and average temperature variations throughout the year. . Definition from Wiktionary, the free dictionary, eDIL: Electronic Dictionary of the Irish Language, Indogermanisches etymologisches Wörterbuch, https://en.wiktionary.org/w/index.php?title=sine&oldid=61390958, Irish terms derived from Proto-Indo-European, Latin terms with Ecclesiastical IPA pronunciation, Latin terms derived from Proto-Indo-European, Norwegian Bokmål terms inherited from Old Norse, Norwegian Bokmål terms derived from Old Norse, Norwegian Bokmål terms with IPA pronunciation, Norwegian Nynorsk terms inherited from Old Norse, Norwegian Nynorsk terms derived from Old Norse, Norwegian Nynorsk terms with IPA pronunciation, Old Irish terms inherited from Proto-Celtic, Old Irish terms derived from Proto-Celtic, Old Irish terms derived from Proto-Indo-European, Scottish Gaelic terms with IPA pronunciation, Scottish Gaelic terms inherited from Old Irish, Scottish Gaelic terms derived from Old Irish, Scottish Gaelic terms inherited from Proto-Celtic, Scottish Gaelic terms derived from Proto-Celtic, Scottish Gaelic terms derived from Proto-Indo-European, Scottish Gaelic terms borrowed from English, Scottish Gaelic terms derived from English, Westrobothnian terms with IPA pronunciation, Requests for translations into Vietnamese, Creative Commons Attribution-ShareAlike License. Discover sine meaning and improve your English skills! ( z θ , and z ⁡ n + Word of the day - in your inbox every day January 15, 2021. ⁡ z Some software libraries provide implementations of sine using the input angle in half-turns, a half-turn being an angle of 180 degrees or Sine definition: a trigonometric function that in a right-angled triangle is the ratio of the length of... | Meaning, pronunciation, translations and examples sin Similarly, Python defines math.sin(x) within the built-in math module. ) What does sine mean in Latin? sin(1022). See more. CPython's math functions call the C math library, and use a double-precision floating-point format. The sine function can also be represented as a generalized continued fraction: The continued fraction representation can be derived from Euler's continued fraction formula and expresses the real number values, both rational and irrational, of the sine function. In contrast, representing 2 Sine squared has only positive values, but twice the number of periods. ) 2 2 π {\sqrt {1+\cos ^{2}(x)}}\,dx} z Some still refer the si- in sine to this root, others refer it to Proto-Indo-European *só (“this”), whence si (“if”). ][8][better source needed]. z Without day; without assigning a day for a further meeting or hearing. x Using only geometry and properties of limits, it can be shown that the derivative of sine is cosine, and that the derivative of cosine is the negative of sine. ( Furthermore, if From Old Irish sine (“old age, seniority, antiquity”), from sen (“old”). 1. (anatomy) A channel for transmitting venous blood. {\displaystyle \mathbb {C} } 1 = The first published use of the abbreviations 'sin', 'cos', and 'tan' is by the 16th century French mathematician Albert Girard; these were further promulgated by Euler (see below). These apply for all values of sine translation in Latin-English dictionary. One can then use the theory of Taylor series to show that the following identities hold for all real numbers x (where x is the angle in radians):[7], If x were expressed in degrees then the series would contain factors involving powers of π/180: if x is the number of degrees, the number of radians is y = πx /180, so, The series formulas for the sine and cosine are uniquely determined, up to the choice of unit for angles, by the requirements that, The radian is the unit that leads to the expansion with leading coefficient 1 for the sine and is determined by the additional requirement that. For example, the C standard library defines sine functions within math.h: sin(double), sinf(float), and sinl(long double). nameless adjective: sine nomine: without name: sine nomine: anonymous adjective: sine nomine, clancularius, anonymus: unnamed adjective: sine nomine, incelebratus, indictus: Find more words! This is a common situation occurring in triangulation, a technique to determine unknown distances by measuring two angles and an accessible enclosed distance. {\displaystyle \pi } ) In site translation mode, Yandex.Translate will translate the entire text content of the site at the URL you provide. π = Sine die is Latin and is defined as indefinitely, or without a future date set. "Jedem das Seine" (German pronunciation: [ˈjeːdm̩ das ˈzaɪ̯nə]) is the literal German translation of the Latin phrase suum cuique, meaning "to each his own" or "to each what he deserves". ) without preposition. The law of sines is useful for computing the lengths of the unknown sides in a triangle if two angles and one side are known. As stated, the value English Translation. Christian hamartiology describes sin as an act of offense against God by despising his persons and Christian biblical law, and by injuring others. ∘ (botany) A notch or depression between two lobes or teeth in the margin of an organ. {\displaystyle 2\pi } The meanings of individual words come complete with examples of usage, transcription, and the possibility to hear pronunciation. {\displaystyle \sin(\alpha )} θ The length of the opposite side of the triangle is simply the y-coordinate. The interchange of the sum and derivative is justified by uniform convergence. ∏ , which can be proved using the Weierstrass M-test. [3], All six trigonometric functions in current use were known in Islamic mathematics by the 9th century, as was the law of sines, used in solving triangles. More modern definitions express the sine as an infinite series, or as the solution of certain differential equations, allowing their extension to arbitrary positive and negative values and even to complex numbers. sine meaning in Hungarian » DictZone Latin-Hungarian dictionary. In general, mathematically important relationships between the sine and cosine functions and the exponential function (see, for example, Euler's formula) are substantially simplified when angles are expressed in radians, rather than in degrees, grads or other units. (pathology) An abnormal cavity or passage such as a fis… α sine mea sententia {adv} ohne mich zu fragen: sine mea sententia {adv} ohne nach meiner Meinung zu fragen: sine pernicie corporis: ohne Schädigung des Körpers: sine ulla spe: ohne jede Hoffnung: 4 Wörter: sine ira et studio: ohne Hass und Parteilichkeit: sine loco et anno > … sine meaning in Hungarian » Latin-Hungarian! 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