z 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. [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]. z 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. 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. 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 = Without the intention of returning. This page was last edited on 26 December 2020, at 04:08. π π From Old Irish sine, siniu, comparative form of sen (“old”). Many other trigonometric functions are also defined in math.h, such as for cosine, arc sine, and hyperbolic sine (sinh). While Latin hasn't been regularly spoken or written for hundreds of years, save for the occasional scholarly text, its legacy is still felt throughout the lexicon of both Romance and Germanic languages today.Whether you're launching an ad hominem attack or adding etcetera to the end of a list, it's likely you're peppering your speech with Latin phrases without even … 1 Kent, Comm. ∞ 2 1. Let f lim This can also be achieved by requiring certain symmetries, and that sine be a periodic function. ) For an angle $${\displaystyle x}$$, the sine function is denoted simply as $${\displaystyle \sin x}$$. 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. What does sine nomine mean in Latin? , we have Turns also have an accuracy advantage and efficiency advantage for computing modulo to one period. Nevettheless, there are those of us who know the difference, who have studied both mathematics and Latin, and so i … x Using the reflection from the calculated geometric derivation of the sine is with the (4n+k)-th derivative at the point 0: This gives the following Taylor series expansion at x = 0. ( Look it up now! In mathematics, the sine is a trigonometric function of an angle. English Translation. 2 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". d a This was transliterated in Arabic as jiba جيب, which however is meaningless in that language and abbreviated jb جب . A legislative body adjourns sine die when it adjourns without appointing a day on which to appear or assemble again. ⁡ (anatomy) A pouch or cavity in any organ or tissue, especially the paranasal sinus. π ⁡ sine meaning in Hungarian » DictZone Latin-Hungarian dictionary (3). sin θ What does sine-die mean? , or, equivalently, as the slope of the line segment. ( ⁡ cos IEEE 754-2008, the most widely used standard for floating-point computation, does not address calculating trigonometric functions such as sine. [12] Roger Cotes computed the derivative of sine in his Harmonia Mensurarum (1722). is the gamma function. b = {\displaystyle \mathbb {C} } absque, extra, citra, sed, set. ) ⁡ π [1] As sine is non-injective, it is not an exact inverse function, but a partial inverse function. cmath.sin(z). Contextual translation of "sine pecunia" into English. Etymologically, the word sine derives from the Sanskrit word for chord, jiva*(jya being its more popular synonym). ⁡ 1 . English Translation. z From: conditio sine qua non in The Oxford Dictionary of Philosophy » Subjects: Philosophy ⁡ 2 . π π {\displaystyle \cos(\theta )={\tfrac {\textrm {adjacent}}{\textrm {hypotenuse}}}} {\displaystyle \mathbb {C} } appear a lot more frequently in literature than the mathematical term "sine." − = Sine die definition is - without any future date being designated (as for resumption) : indefinitely. 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 {\displaystyle \textstyle {\sum _{n=1}^{\infty }|a_{n}(z)|}} Alternatively, the infinite product for the sine can be proved using complex Fourier series. The arc length for a full period is 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). α C ( SINE Latin: Withou. n 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. , the sine function is denoted simply as ) A similar argument can be made for the cosine function to show that = = / Using complex Fourier series, the function a 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. [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. ( − ( {\displaystyle \sin(\alpha )} Initial mutations of a following adjective: Gregory Toner, Maire Ní Mhaonaigh, Sharon Arbuthnot, Dagmar Wodtko, Maire-Luise Theuerkauf, editors (2019) , “. d z Representing angles in turns or half-turns has accuracy advantages and efficiency advantages in some cases. {\displaystyle {\tfrac {\sin(\theta )}{\cos(\theta )}}} Discover sine meaning and improve your English skills! radians. {\displaystyle \textstyle {\prod _{n=1}^{\infty }(1+a_{n}(z))}} 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. The function of sine and versine (1 - cosine) can be traced to the jyā and koṭi-jyā functions used in Gupta period (320 to 550 CE) Indian astronomy (Aryabhatiya, Surya Siddhanta), via translation from Sanskrit to Arabic and then from Arabic to Latin. / + 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 , then the function ( For arguments outside those in the table, one may compute the corresponding information by using the periodicity {\displaystyle \ln(\sin(\pi z))+C_{0}} 2. 2 times x, plus a correction [3] The word "sine" (Latin "sinus") comes from a Latin mistranslation by Robert of Chester of the Arabic jiba, which is a transliteration of the Sanskrit word for half the chord, jya-ardha.[4]. = {\displaystyle \sin(\alpha +360^{\circ })=\sin(\alpha )} Sine die is Latin and is defined as indefinitely, or without a future date set. SINE Meaning: "Horologiographia, the Art of Dialling"), from Latin sinus "fold in a garment, bend, curve, bosom" (see… See definitions of sine. [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. 1 n Using the unit circle definition has the advantage that the angle can be extended to any real argument. As stated, the value 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"). Use * for blank tiles (max 2) Advanced Search Advanced Search: Use * for blank spaces … e . n appear a lot more frequently in literature than the mathematical term "sine." sin And as sometimes nesi was also written, with -ne being nē (“not”), sine might literally mean "not this". opposite . During World War II the phrase was cynically used by the Nazis as a motto displayed over the entrance of Buchenwald concentration camp. {\displaystyle {\frac {\pi }{2}}} {\displaystyle b} sine controversia adverb: kétségkívül határozószó. We all went on Monday Evening to the sea shore, to see the sceneDrawn: thi… From the Latin translation of the Vulgate Bible of Psalm 130, of which it is a traditional title in Roman Catholic liturgy. d 2 π ( 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. {\displaystyle \blacksquare }. = appears to depend on the choice of right triangle containing an angle of measure α. … a ) 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. 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. π of the sine function. C Most of the examplea given are uses of the unrelated Latin word "sine," meaning "without." ) ⁡ Animation showing how the sine function (in red) ⁡ The parameter of each is a floating point value, specifying the angle in radians. (anatomy) A channel for transmitting venous blood. Some still refer the si- in sine to this root, others refer it to Proto-Indo-European *só (“this”), whence si (“if”). 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. The word sine defined here is the mathematical one, derived from the Latin "sinus." The Opus palatinum de triangulis of Georg Joachim Rheticus, a student of Copernicus, was probably the first in Europe to define trigonometric functions directly in terms of right triangles instead of circles, with tables for all six trigonometric functions; this work was finished by Rheticus' student Valentin Otho in 1596. Some software libraries provide implementations of sine using the input angle in half-turns, a half-turn being an angle of 180 degrees or Christian hamartiology describes sin as an act of offense against God by despising his persons and Christian biblical law, and by injuring others. {\displaystyle 2\pi } . 2 years ago. ⁡ In contrast, representing sin → n ∞ C For example, the C standard library defines sine functions within math.h: sin(double), sinf(float), and sinl(long double). Some still refer the si- in sine to this root, others refer it to Proto-Indo-European *só (“this”), whence si (“if”). ⁡ It follows that the infinite product is holomorphic on Each function returns the same data type as it accepts. 2 In trigonometry, a unit circle is the circle of radius one centered at the origin (0, 0) in the Cartesian coordinate system. The word sine defined here is the mathematical one, derived from the Latin "sinus." Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License The ratio of the length of the side opposite an acute angle in a right triangle to the length of the hypotenuse. ⁡ In mathematics, the sine is a trigonometric function of an angle. = Quell Learn more >> … − Latin Hungarian; coniugium sine prole, est quasi dies sine sole: házasság gyermek nélkül olyan, mint a nappal napsütés nélkül For an angle ( It is a simplified version of Latin, and retains its vocabulary. ( 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”). z 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). ∏ 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. This is an entire function. cos Γ Human translations with examples: near, money, without, pecuniary, i need money, without money, money is evil. θ The interchange of the sum and derivative is justified by uniform convergence. 2 = α "Sine qua non" "sine die," etc. Sine can also take a complex number as an argument. Since In computing, it is typically abbreviated to sin. Proof of the infinite product for the sine, Partial fraction and product expansions of complex sine, Jacques Sesiano, "Islamic mathematics", p. 157, in, Grand Challenges of Informatics, Paul Zimmermann. The graph shows both the sine function and the sine squared function, with the sine in blue and sine squared in red. ∫ ) ( + The actions are so obvious … {\displaystyle f} Sine definition: a trigonometric function that in a right-angled triangle is the ratio of the length of... | Meaning, pronunciation, translations and examples The inverse function of sine is arcsine (arcsin or asin) or inverse sine (sin-1). 4 Hence, for some open and connected subset of ⁡ 2 In site translation mode, Yandex.Translate will translate the entire text content of the site at the URL you provide. Without day; without assigning a day for a further meeting or hearing. Complex sine functions are also available within the cmath module, e.g. More meanings for sine. Alle weiteren Informationen findest du im Haupteintrag sin. sine (stressed reflexive-accusative form of el, ea, ei, and ele), sine f (genitive singular sine, plural sinean). CPython's math functions call the C math library, and use a double-precision floating-point format. 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. sin(z) is found in the functional equation for the Gamma function. September 20, 2006 – p. 14/31, List of integrals of trigonometric functions, Differentiation of trigonometric functions, Trigonometric functions § Relationship to exponential function (Euler's formula), "Why are the phase portrait of the simple plane pendulum and a domain coloring of sin(z) so similar? = π Γ {\displaystyle \sin(\theta )={\tfrac {\textrm {opposite}}{\textrm {hypotenuse}}}={\tfrac {\textrm {opposite}}{1}}={\textrm {opposite}}} 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. can be decomposed as, Setting hypotenuse opposite θ This allows results to be looked up from a table rather than being calculated in real time. [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. Sine squared has only positive values, but twice the number of periods. {\textstyle {\frac {4{\sqrt {2\pi ^{3}}}}{\Gamma (1/4)^{2}}}+{\frac {\Gamma (1/4)^{2}}{\sqrt {2\pi }}}=7.640395578\ldots } n [9] Al-Khwārizmī (c. 780–850) produced tables of sines, cosines and tangents. With this restriction, for each x in the domain, the expression arcsin(x) will evaluate only to a single value, called its principal value. . It follows that the arcsine function is multivalued: arcsin(0) = 0, but also arcsin(0) = π, arcsin(0) = 2π, etc. Sine Die [Latin, Without day.] ⁡ "Sine qua non" "sine die," etc. converges uniformly on any closed disk, x tan(θ) is then defined as As a holomorphic function, sin z is a 2D solution of Laplace's equation: The complex sine function is also related to the level curves of pendulums.[how? = It follows that, Since z z 7.640395578 [19] Similarly, one can show that, Using product expansion technique, one can derive. z sin π 2 {\displaystyle \pi } Most of the examplea given are uses of the unrelated Latin word "sine," meaning "without." converges uniformly on any closed disk as well. {\displaystyle x=\pi } {\displaystyle y=\sin(\theta )} ⁡ cos ∏ z cos z .[1][2]. / cot 1 + x {\displaystyle x} π ) in binary floating-point or binary scaled fixed-point always involves a loss of accuracy. DAMNUM SINE INJURIA Latin meaning Damage without legal injury. without a name More meanings for sine nomine. {\displaystyle 2\pi } C 4. Some still refer the si-in sine to this root, others refer it to Proto-Indo-European *só‎ ("this") (whence si‎ ("if")). 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. [18] Algorithms for calculating sine may be balanced for such constraints as speed, accuracy, portability, or range of input values accepted. n π ) The name Sine is in the following categories: Celtic Names, Gaelic Names, Irish Names. 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