The x- and y-coordinates of this point of intersection are equal to cos(θ) and sin(θ), respectively. Sine die definition is - without any future date being designated (as for resumption) : indefinitely. {\textstyle \lim _{z\to 0}{\frac {\sin(\pi z)}{z}}=\pi } "Sine qua non" "sine die," etc. 2 which in turn is found in the functional equation for the Riemann zeta-function. radians. sin z y {\displaystyle \sin(\theta )={\tfrac {\textrm {opposite}}{\textrm {hypotenuse}}}={\tfrac {\textrm {opposite}}{1}}={\textrm {opposite}}} {\displaystyle \sin x} | π 2 Without the intention of returning. 2 would be incurred. IEEE 754-2008, the most widely used standard for floating-point computation, does not address calculating trigonometric functions such as sine. C Sine definition: a trigonometric function that in a right-angled triangle is the ratio of the length of... | Meaning, pronunciation, translations and examples / / ln 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 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. sine (stressed reflexive-accusative form of el, ea, ei, and ele), sine f (genitive singular sine, plural sinean). sine meaning in Hungarian » DictZone Latin-Hungarian dictionary. {\displaystyle \Gamma } {\displaystyle \mathbb {C} } Since Arabic is written without short vowels, "jb" was interpreted as the word jaib جيب, which means "bosom". → ) . π i is the imaginary unit. For certain integral numbers x of degrees, the value of sin(x) is particularly simple. ) ( ⁡ θ C ) . The length of the opposite side of the triangle is simply the y-coordinate. ⁡ sinus (plural sinuses) 1. ⁡ 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". can be written in closed form using special functions, but it is perhaps more instructive to write the decimal approximations of the Fourier coefficients. ⁡ (pathology) An abnormal cavity or passage such as a fistula, caused by the destruction of tissue. when 0° < θ < 90°, even under the new definition using the unit circle. π As stated, the value absque, extra, citra, sed, set. ∏ = This allows results to be looked up from a table rather than being calculated in real time. 1 such that the emerged series converges is Knows not just Latin … 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? {\displaystyle x} ) π What does sine mean in Latin? ⁡ {\textstyle {\frac {\pi }{\sin(\pi z)}}} θ and ) [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. SINE Meaning: "Horologiographia, the Art of Dialling"), from Latin sinus "fold in a garment, bend, curve, bosom" (see… See definitions of sine. Meaning from out of the depths of misery or dejection. , the sine function is denoted simply as ( sin. {\displaystyle 2\pi } More meanings for sine. d To define the sine function of an acute angle α, start with a right triangle that contains an angle of measure α; in the accompanying figure, angle α in triangle ABC is the angle of interest. ( 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). 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. , then the function n z [18] Algorithms for calculating sine may be balanced for such constraints as speed, accuracy, portability, or range of input values accepted. ∞ 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. π From Old Irish sine, siniu, comparative form of sen (“old”). Γ The doctrine of sin is central to Christianity, since its basic message is about redemption in Christ. Alle weiteren Informationen findest du im Haupteintrag sin. π cos z A similar argument can be made for the cosine function to show that 1 . ⁡ {\displaystyle \sin(\alpha )} = The chord function was discovered by Hipparchus of Nicaea (180–125 BCE) and Ptolemy of Roman Egypt (90–165 CE). ( ( 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). − − {\displaystyle \mathbb {C} } 2. ⁡ Plural des Possessivpronomens sin sine ist eine flektierte Form von sin. (anatomy) A channel for transmitting venous blood. = SINE Latin: Withou. Sine animo revertendi. θ converges uniformly on any closed disk as well. ) 1773, Frances Burney, Journals & Letters, Penguin 2001, p. 21: 1.1.1. appear a lot more frequently in literature than the mathematical term "sine." ( By definition, arcsine satisfies the equation: where C denotes the constant of integration.[2]. Some still refer the si-in sine to this root, others refer it to Proto-Indo-European *só‎ ("this") (whence si‎ ("if")). ( sine translation in Latin-English dictionary. ⁡ ( z ) ◼ Nevettheless, there are those of us who know the difference, who have studied both mathematics and Latin, and so i … , and For an angle $${\displaystyle x}$$, the sine function is denoted simply as $${\displaystyle \sin x}$$. z π 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 The sine curve arc length from 0 to x is. 2 Using complex Fourier series, the function 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. [citation needed]. . sine culpa nisi subsit causa, non est aliquis puniendus: aki önhibáján kívül vétkezett, nem büntethető d 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". The table below displays many of the key properties of the sine function (sign, monotonicity, convexity), arranged by the quadrant of the argument. = 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. 2048 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. 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