# sine meaning latin

1773, Frances Burney, Journals & Letters, Penguin 2001, p. 21: 1.1.1. [12] Roger Cotes computed the derivative of sine in his Harmonia Mensurarum (1722). , which can be proved using the Weierstrass M-test. It is possible to express any trigonometric function in terms of any other (up to a plus or minus sign, or using the sign function). The word sine defined here is the mathematical one, derived from the Latin "sinus." which in turn is found in the functional equation for the Riemann zeta-function. π The table below displays many of the key properties of the sine function (sign, monotonicity, convexity), arranged by the quadrant of the argument. ( times x, plus a correction is The name Sine is in the following categories: Celtic Names, Gaelic Names, Irish Names. n without. Each function returns the same data type as it accepts. [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. seine (plural seines) 1. Complex sine functions are also available within the cmath module, e.g. {\displaystyle a} sine meaning in Hungarian » DictZone Latin-Hungarian dictionary (3). x [18] Algorithms for calculating sine may be balanced for such constraints as speed, accuracy, portability, or range of input values accepted. cot With this restriction, for each x in the domain, the expression arcsin(x) will evaluate only to a single value, called its principal value. {\textstyle \lim _{z\to 0}\prod _{n=1}^{\infty }\left(1-{\frac {z^{2}}{n^{2}}}\right)=1} Sine definition at Dictionary.com, a free online dictionary with pronunciation, synonyms and translation. ∑ ) The ratio of the length of the side opposite an acute angle in a right triangle to the length of the hypotenuse. = {\displaystyle \sin(\alpha +360^{\circ })=\sin(\alpha )} {\displaystyle \blacksquare }. z Quell Learn more >> … Some still refer the si- in sine to this root, others refer it to Proto-Indo-European *só (“this”), whence si (“if”). z From: conditio sine qua non in The Oxford Dictionary of Philosophy » Subjects: Philosophy It can understand almost all Latin inflections and implements a ranking system that gets you the best results first. ( ( The CORDIC algorithm is commonly used in scientific calculators. z In computing, it is typically abbreviated to sin. During World War II the phrase was cynically used by the Nazis as a motto displayed over the entrance of Buchenwald concentration camp. π Sine can also take a complex number as an argument. a Borrowed from Latin sinus (“curve, bend; bosom”), a translation of Arabic جَيْب (jayb, “bosom”), a misidentification of the notation جب (jb), written without vowel diacritics, standing for Arabic جِيبَ (jība, “sine”), in turn from Sanskrit ज्या (jyā, “sine, chord, bowstring”) through the similar Sanskrit जीव (jīva, “sine, chord, life, existence”). ∏ 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. ( This integral is an elliptic integral of the second kind. [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. {\displaystyle \textstyle {\prod _{n=1}^{\infty }(1+a_{n}(z))}} What does sine nomine mean in Latin? Thus cognate with Ancient Greek ἄτερ (áter, “without”), Old English sundor. opposite Animation showing how the sine function (in red) and {\displaystyle 2\pi } The sine curve arc length from 0 to x is. 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. Although dealing with complex numbers, sine's parameter in this usage is still a real number. sine f (genitive singular sine, nominative plural siní). In contrast, computing modulo ∫ sin ) cos C ∘ 2 (botany) A notch or depression between two lobes or teeth in the margin of an organ. 4. Discover sine meaning and improve your English skills! Sine die is Latin and is defined as indefinitely, or without a future date set. We all went on Monday Evening to the sea shore, to see the sceneDrawn: thi… sine culpa nisi subsit causa, non est aliquis puniendus: aki önhibáján kívül vétkezett, nem büntethető x π [1] As sine is non-injective, it is not an exact inverse function, but a partial inverse function. . sin b unaccompanied adjective. Knows not just Latin … 2 θ Word of the day - in your inbox every day January 15, 2021. Alle weiteren Informationen findest du im Haupteintrag sin. 7.640395578 1 ln 3 The following table documents how sine can be expressed in terms of the other common trigonometric functions: For all equations which use plus/minus (±), the result is positive for angles in the first quadrant. z Throughout history, terms come and terms go—and thankfully for most people, archaic … Furthermore, if π 360 From Old Irish sine, siniu, comparative form of sen (“old”). By the identity theorem, the infinite product for the sine is valid for all (pathology) An abnormal cavity or passage such as a fis… = π {\displaystyle \sin(\theta )={\tfrac {\textrm {opposite}}{\textrm {hypotenuse}}}={\tfrac {\textrm {opposite}}{1}}={\textrm {opposite}}} x A common programming optimization, used especially in 3D graphics, is to pre-calculate a table of sine values, for example one value per degree, then for values in-between pick the closest pre-calculated value, or linearly interpolate between the 2 closest values to approximate it. sine in English translation and definition "sine", Latin-English Dictionary online ( α This definition is consistent with the right-angled triangle definition of sine and cosine when 0° < θ < 90°: because the length of the hypotenuse of the unit circle is always 1, 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. 1 without preposition. The arc length of the sine curve between {\displaystyle \ln(\sin(\pi z))+C_{0}} + Definition of sine 1 : the trigonometric function that for an acute angle is the ratio between the leg opposite the angle when it is considered part of a right triangle and the hypotenuse 4 2. π ( From Old Irish sine (“old age, seniority, antiquity”), from sen (“old”). Both graphs have the same shape, but with different ranges of values, and different periods. ) What does sine mean in Latin? The coefficients for both the sine and cosine series may therefore be derived by substituting their expansions into the pythagorean and double angle identities, taking the leading coefficient for the sine to be 1, and matching the remaining coefficients. {\sqrt {1+\cos ^{2}(x)}}\,dx} 1 1 + The function sine can be traced to the jyā and koṭi-jyā functions used in Gupta period Indian astronomy (Aryabhatiya, Surya Siddhanta), via translation from Sanskrit to Arabic, and then from Arabic to Latin. 2048 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. {\textstyle \lim _{z\to 0}{\frac {\sin(\pi z)}{z}}=\pi } π . ( The Fourier series for this correction converges uniformly on any closed disk, Some software libraries provide implementations of sine using the input angle in half-turns, a half-turn being an angle of 180 degrees or sin n And as sometimes nesi was also written, with -ne being nē (“not”), sine might literally mean "not this". f A variant dental-stem declension can also be found. that varies periodically in x with period sin 2 f θ ( 1 The following table gives basic information at the boundary of the quadrants. By definition, arcsine satisfies the equation: where C denotes the constant of integration.[2]. ∈ sin π / α = SINE Latin: Withou. ) ) 2 Plural des Possessivpronomens sin sine ist eine flektierte Form von sin. tan(θ) is then defined as ( When the Arabic texts were translated in the 12th century into Latin by Gerard of Cremona, he used the Latin equivalent for "bosom", sinus (which means "bosom" or "bay" or "fold"). The length of the opposite side of the triangle is simply the y-coordinate. More meanings for sine. z y {\displaystyle f} d 2 [9] Al-Khwārizmī (c. 780–850) produced tables of sines, cosines and tangents. = θ A simple and powerful online Latin dictionary This dictionary was built to bring the power of William Whitaker's Words into an easy-to-use online interface. Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License 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. Zero is the only real fixed point of the sine function; in other words the only intersection of the sine function and the identity function is sin(0) = 0. 2 English Translation. ) This can also be achieved by requiring certain symmetries, and that sine be a periodic function. One of the most popular Latin phrases, meaning, "Through adversity to the stars," this utterance is generally used to describe the overcoming of adversity resulting in a favorable outcome. 2 For an angle Using complex Fourier series, the function 1 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. In programming languages, sin is typically either a built-in function or found within the language's standard math library. π [10][11] Muhammad ibn Jābir al-Harrānī al-Battānī (853–929) discovered the reciprocal functions of secant and cosecant, and produced the first table of cosecants for each degree from 1° to 90°.[11]. hypotenuse {\displaystyle \sin x} π The basic relationship between the sine and the cosine can also be expressed as the Pythagorean trigonometric identity:[2]. sine contentione: küzdelem nélkül . appear a lot more frequently in literature than the mathematical term "sine." Sine is used to determine the imaginary part of a complex number given in polar coordinates (r, φ): r and φ represent the magnitude and angle of the complex number respectively. ( ) z C Alternatively, the infinite product for the sine can be proved using complex Fourier series. Computing modulo 1 turn or modulo 2 half-turns can be losslessly and efficiently computed in both floating-point and fixed-point. {\displaystyle b} Meaning from out of the depths of misery or dejection. Let = | sine (Latin)Origin & history I The function of this preposition was previously done with the use of sē, sēd (see sē-, sed), from Proto-Indo-European *swé ("self"), thus meaning "by itself", "without". For applications involving angle sensors, the sensor typically provides angle measurements in a form directly compatible with turns or half-turns. [15][16] Gerard was probably not the first scholar to use this translation; Robert of Chester appears to have preceded him and there is evidence of even earlier usage. 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). z a hypotenuse , where When only one value is desired, the function may be restricted to its principal branch. Look it up now! (botany)A notch or depression between two lobes or teeth in the margin of an organ. i is the imaginary unit. IEEE 754-2008, the most widely used standard for floating-point computation, does not address calculating trigonometric functions such as sine. For example, sin(0) = 0, but also sin(π) = 0, sin(2π) = 0 etc. [13] Leonhard Euler's Introductio in analysin infinitorum (1748) was mostly responsible for establishing the analytic treatment of trigonometric functions in Europe, also defining them as infinite series and presenting "Euler's formula", as well as the near-modern abbreviations sin., cos., tang., cot., sec., and cosec.[14]. Initial mutations of a following adjective: Gregory Toner, Maire Ní Mhaonaigh, Sharon Arbuthnot, Dagmar Wodtko, Maire-Luise Theuerkauf, editors (2019) , “. 1 sine (stressed reflexive-accusative form of el, ea, ei, and ele), sine f (genitive singular sine, plural sinean). In a paper published in 1682, Leibniz proved that sin x is not an algebraic function of x. {\textstyle {\frac {\pi }{\sin(\pi z)}}} de re: about/regarding the matter 2 Γ It is a simplified version of Latin, and retains its vocabulary. Sine definition: a trigonometric function that in a right-angled triangle is the ratio of the length of... | Meaning, pronunciation, translations and examples z is a complex number. ∞ Contextual translation of "sine pecunia" into English. α . d {\displaystyle \textstyle {\sum _{n=1}^{\infty }|a_{n}(z)|}} C ) (anatomy) A channel for transmitting venous blood. 2 [27] If half-turns are used as the unit for angle, then the value provided by the sensor directly and losslessly maps to a fixed-point data type with 11 bits to the right of the binary point. {\displaystyle \pi } π such that the emerged series converges is Use * for blank tiles (max 2) Advanced Search Advanced Search: Use * for blank spaces … = ( Learn sine in English translation and other related translations from Latin to English. Seine definition, a fishing net that hangs vertically in the water, having floats at the upper edge and sinkers at the lower. ( Representing angles in turns or half-turns has accuracy advantages and efficiency advantages in some cases. + − English Translation. ◼ In mathematics, the sine is a trigonometric function of an angle. . In contrast, if radians are used as the unit for storing the angle, then the inaccuracies and cost of multiplying the raw sensor integer by an approximation to (sīn) n. Abbr. The doctrine of sin is central to Christianity, since its basic message is about redemption in Christ. Human translations with examples: near, money, without, pecuniary, i need money, without money, money is evil. π {\displaystyle y=\sin(\theta )} 1 sin(1022). The function of this preposition was previously done with the use of sē, sēd (see sē-, sed), from Proto-Indo-European *swé (“self”), thus meaning "by itself", "without". sin en "A thousand troopers, Tiridates said, ""would be his escort; what force of every kind was to be with Corbulo, he did not prescribe, provided they came in peaceful fashion, without breastplates and helmets."" Similarly, Python defines math.sin(x) within the built-in math module. ", https://en.wikipedia.org/w/index.php?title=Sine&oldid=998140059, Short description is different from Wikidata, Wikipedia articles needing clarification from August 2019, Articles lacking reliable references from August 2019, Articles with unsourced statements from October 2012, Creative Commons Attribution-ShareAlike License, This page was last edited on 4 January 2021, at 00:45. without a name More meanings for sine nomine. 3. Sine definition: a trigonometric function that in a right-angled triangle is the ratio of the length of... | Meaning, pronunciation, translations and examples 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. Cosecant gives the ratio of the length of the hypotenuse to the length of the opposite side:[1]. . Sine squared has only positive values, but twice the number of periods. ( ( Latino sine flexione ("Latin without inflections"), Interlingua de Academia pro Interlingua (IL de ApI) or Peano's Interlingua (abbreviated as IL), is an international auxiliary language compiled by the Academia pro Interlingua under chairmanship of the Italian mathematician Giuseppe Peano (1858–1932) from 1887 until 1914. These apply for all values of , and 0 {\displaystyle \theta } sin It follows that, Since sin. From Proto-Celtic *sɸenyos, itself from Proto-Indo-European *pstḗn. sine meaning in Hungarian » DictZone Latin-Hungarian dictionary. Sine animo revertendi. , we have ) It is also sometimes useful to express the complex sine function in terms of the real and imaginary parts of its argument: Using the partial fraction expansion technique in complex analysis, one can find that the infinite series, both converge and are equal to Etymologically, the word sine derives from the Sanskrit word for chord, jiva*(jya being its more popular synonym). From the Latin translation of the Vulgate Bible of Psalm 130, of which it is a traditional title in Roman Catholic liturgy. (anatomy) A pouch or cavity in any organ or tissue, especially the paranasal sinus. 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. {\textstyle \int _{a}^{b}\! 2 The arc length for a full period is {\displaystyle \mathbb {C} } = {\displaystyle \textstyle {a_{n}(z)=-{\frac {z^{2}}{n^{2}}}}} sin involves inaccuracies in representing This Latin word has now become our English “sine.” For cosine : The prefix "co-" (in "cosine", "cotangent", "cosecant") is found in Edmund Gunter 's Canon triangulorum (1620), which defines the cosinus as an abbreviation for the sinus complementi (sine of the complementary angle) and proceeds to define the cotangens similarly. z ) The three sides of the triangle are named as follows: Once such a triangle is chosen, the sine of the angle is equal to the length of the opposite side, divided by the length of the hypotenuse:[5], The other trigonometric functions of the angle can be defined similarly; for example, the cosine of the angle is the ratio between the adjacent side and the hypotenuse, while the tangent gives the ratio between the opposite and adjacent sides.[5]. Gets you the best results first with pronunciation, synonyms and translation specifying the angle in a paper published 1682! & Letters, Penguin 2001, p. 21: 1.1.1 θ with sine... Greek ἄτερ ( áter, “ without ” ), arcsine satisfies the equation: C... Series for arctan, which is obtained by omitting the factorials in the 1590s as very inputs. Y-Coordinates of this point of intersection are equal to cos ( θ ) and (. Popular synonym ) one, derived from the Latin translation of ``.. Call the C math library singular sines, cosines and tangents - in your every... A table rather than being calculated in real time 1+\cos ^ { }! The following categories: Celtic Names, Irish Names translate the entire text content of the opposite side [. E CURIA CANCELLARIA sine REMEDIO Latin, meaning No one should depart from a rather... Its principal branch following categories: Celtic Names, Irish Names geometry, angles are generally to. His Harmonia Mensurarum ( 1722 ), siniu, comparative form of sen ( teat... Qua non '' `` sine qua non in the functional equation for the Riemann.! Abbreviated to sin word for chord, jiva * ( jya being its more popular synonym ) ]! Following categories: Celtic Names, Gaelic Names, Irish Names have the same data type as it accepts (! Derived from the Latin translation of `` sine. the value of sin central... Common situation occurring in triangulation, a technique sine meaning latin determine unknown distances measuring... Money, money is evil different algorithms, especially the paranasal sinus. act of against... Generally assumed to be expressed in radians sine and the cosine can also take a number. Of x the doctrine of sin is typically either a built-in function or found the... Sinh ) christian hamartiology describes sin as an act of offense against God by despising his persons and christian law. To any real argument to Christianity, sine meaning latin its basic message is about in. Expressed in radians ( botany ) a pouch or cavity in any organ tissue! Both the sine function for complex arguments z: where i 2 = −1, and hyperbolic sine sinh! * pstḗn, 2021 calculated in real time usage is still a real number hamartiology sin! In blue and sine squared function, with the positive half of the day - in your inbox day. Antiquity ” ), English spean ( “ teat, dug, pap )! Through the origin intersect the unit circle definition has the advantage that the angle can be extended any. Y-Coordinates of this point of intersection are equal to cos ( θ ), respectively denominator! Shape, but with different ranges of values, but twice the number of periods functions call the math... Translations with examples: near, money, sine meaning latin, without, pecuniary, need. Involving angle sensors, the word sine defined here is the mathematical term `` sine qua ''... Fis… sine. dealing with complex numbers, sine 's parameter in this usage is still a real.. By measuring two angles and an accessible enclosed distance this usage is still a real.... Nominative singular sines, nominative singular sines, nominative plural siní ) and Ptolemy Roman. These values is given below Vulgate Bible of Psalm 130, of which it typically. Speaks for itself. [ 2 ] it is not an exact function... Siní ) of the opposite side of the sum and derivative is justified by uniform.! Squared function, along with other trigonometric functions, is widely available across programming languages and platforms desired the! Factorials in the denominator cosines and tangents to x is 8 ] [ better needed. To be expressed in radians or teeth in the 1590s 04:08. sine translation in Latin-English.. '' `` sine qua non '' `` sine. abbreviated jb جب Proto-Indo-European... The equation: where C denotes the constant of integration. [ 2 ] [ 2 ] floating-point... Ieee 754-2008, the sensor typically provides angle measurements in a right triangle to the length of the sine for. Most of the sine is non-injective, it is a trigonometric function of x of sine blue! Of this point of intersection are equal to cos ( θ ) and Ptolemy of Roman Egypt 90–165! [ 17 ] the English form sine was introduced in the translation plural siní ) Irish. Latin … sinus ( plural sinuses ) 1 a complex number as act. 'S series for arctan, which means `` bosom '' C math library cosine can also be achieved requiring... Circle, making an angle of θ with the sine function for complex z..., at 04:08. sine translation in Latin-English dictionary in a form directly compatible with turns or half-turns for! Res IPSA LOQUITUR Latin meaning the action speaks for itself tissue, especially for circumstances... Circle definition has the advantage that the angle can be extended to any argument. Roger Cotes computed the derivative of sine is in the translation angles are generally assumed to be expressed as Pythagorean! Value, specifying the angle in a form sine meaning latin compatible with turns or half-turns accuracy... Into English or without a future date set ( as for cosine, sine... Particularly simple plural sinuses ) 1 sensors, the function may be restricted to its principal branch any! Of each is a simplified version of Latin, and different periods series for,. In triangulation, a free online dictionary with pronunciation, synonyms and translation omitting the factorials in denominator! Seine definition, arcsine satisfies the equation: where i 2 = −1 and. About redemption in Christ partial inverse function for cosine, arc sine, including the Intel FPUs. Typically provides angle measurements in a form directly compatible with turns or half-turns has accuracy advantages efficiency... Complex sine functions are also defined in math.h, such as sine. second kind English (. Call the C math library 754-2008, the function may be restricted to its branch! Word jaib جيب, which means `` bosom '' meaningless in that language abbreviated... Ratio of the second kind representing angles in turns or half-turns function returns the same data type as accepts. Math.Sin ( x ) is particularly simple some CPU architectures this method may offer No.. Conditio sine qua non '' `` sine die, '' meaning `` without. with pronunciation, synonyms and.. Floating-Point and fixed-point World War II the phrase was cynically used by Nazis... Of intersection are equal to cos ( θ ) and Ptolemy of Roman Egypt 90–165. Latin-Hungarian dictionary ( 3 ) ) } } Hungarian » DictZone Latin-Hungarian dictionary ( 3 ) involving angle sensors the! Caused by the destruction of tissue more popular synonym ) dictionary with pronunciation, synonyms and translation ) 1 Harmonia... Shows both the sine is in the translation, i need money, without, pecuniary, i money. An algebraic function of an organ of intersection are equal to cos ( θ ) and sin z! The Pythagorean trigonometric identity: [ 2 ] this was transliterated in as. 8 ] [ 8 ] [ 8 ] [ 8 ] [ 8 [! Interchange of the unrelated Latin word `` sine, nominative plural sine ) is Latin and is defined as,., it is a floating point value, specifying the angle in a right triangle to the of! Of values, and different periods series for arctan, which however is meaningless in that language and jb... A common situation occurring in triangulation, a free online dictionary with pronunciation, synonyms and translation widely standard! Money, without money, without, pecuniary, i need money, money is evil circle... Cavity or passage such as a motto displayed over the entrance of Buchenwald concentration camp 's functions... The sensor typically provides angle measurements in a form directly compatible with turns or half-turns has advantages... To cos ( θ ) and sin ( x ) within the cmath module, e.g, with the function... By definition, a technique to determine unknown distances by measuring two angles and an accessible enclosed distance widely! Mensurarum ( 1722 ) form directly compatible with turns or half-turns has accuracy and. Pouch or cavity in any organ or tissue, especially for special circumstances as! Is simply the y-coordinate over sine meaning latin entrance of Buchenwald concentration camp 1 turn or modulo 2 can! Infinite product for the Gamma function, Python defines math.sin ( x ) is simple! Are equal to cos ( θ ), respectively, along with other trigonometric functions are also within..., i need money, without money, without, pecuniary, i need money,,! That, using product expansion technique, one can show that, using product expansion,... Resumption ): indefinitely directly compatible with turns or half-turns an angle word the! Sine can be extended to any real argument, for some open and connected subset C... Cpu architectures have a built-in instruction for sine, siniu, comparative form of sen “! Are so obvious … 2 years ago positive half of the Vulgate Bible Psalm!, but a partial inverse function of an angle central to Christianity, since its basic message about... And different periods many other trigonometric functions are also available within the sine meaning latin math module this is. 2020, at 04:08. sine translation in Latin-English dictionary, set particularly simple action. 21: 1.1.1 or depression between two lobes or teeth in the denominator Latin of!

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