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120 relations: Albert Girard, Algebraic function, Angle, Arabic, Aryabhatiya, Āryabhaṭa's sine table, İznik, Bantam Books, Bhaskara I's sine approximation formula, C (programming language), C mathematical functions, C standard library, Cartesian coordinate system, Chord (geometry), Circumscribed circle, Complex analysis, Complex number, Constant of integration, Convex function, CORDIC, CPython, Data type, Degree (angle), Derivative, Differential equation, Discrete sine transform, Double-precision floating-point format, Egypt (Roman province), Entire function, Etymology, Euler's continued fraction formula, Euler's formula, Exponential function, Fixed point (mathematics), Floating-point arithmetic, Fourier series, Functional equation, Gamma function, Generalized continued fraction, Generalized trigonometry, Georg Joachim Rheticus, Gerard of Cremona, Gottfried Wilhelm Leibniz, Gradian, Gregory's series, Gupta Empire, Hipparchus, Holomorphic function, Hyperbolic function, Hypotenuse, ..., Identity function, IEEE 754 revision, Imaginary unit, Indian astronomy, Inflection point, Injective function, Integer, Inverse function, Inverse trigonometric functions, Irrational number, Jyā, koti-jyā and utkrama-jyā, Laplace's equation, Latin, Law of sines, Legendre form, Leonhard Euler, Limit of a function, List of periodic functions, List of trigonometric identities, Long double, Madhava series, Madhava's sine table, Mathematics, Maxima and minima, Medieval Latin, Merriam-Webster, Monotonic function, Multiplicative inverse, Nicolaus Copernicus, Optical sine theorem, Periodic function, Polar coordinate system, Polar sine, Principal branch, Principal value, Proofs of trigonometric identities, Ptolemy, Pythagorean trigonometric identity, Python (programming language), Radian, Rational number, Real number, Riemann zeta function, Right triangle, Roger Cotes, Sanskrit, Series (mathematics), Sign (mathematics), Sign function, Similarity (geometry), Sinc function, Sine and cosine transforms, Sine quadrant, Sine wave, Sine-Gordon equation, Single-precision floating-point format, Sinusoidal model, Sound, Surya Siddhanta, Taylor series, Transliteration, Triangle, Triangulation, Trigonometric functions, Trigonometric integral, Trigonometry, Turn (geometry), Unit circle, Uta Merzbach, Zero of a function. Expand index (70 more) »
Albert Girard
Albert Girard (1595 in Saint-Mihiel, France − 8 December 1632 in Leiden) was a French-born mathematician.
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Algebraic function
In mathematics, an algebraic function is a function that can be defined as the root of a polynomial equation.
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Angle
In plane geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
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Arabic
Arabic (العَرَبِيَّة) or (عَرَبِيّ) or) is a Central Semitic language that first emerged in Iron Age northwestern Arabia and is now the lingua franca of the Arab world. It is named after the Arabs, a term initially used to describe peoples living from Mesopotamia in the east to the Anti-Lebanon mountains in the west, in northwestern Arabia, and in the Sinai peninsula. Arabic is classified as a macrolanguage comprising 30 modern varieties, including its standard form, Modern Standard Arabic, which is derived from Classical Arabic. As the modern written language, Modern Standard Arabic is widely taught in schools and universities, and is used to varying degrees in workplaces, government, and the media. The two formal varieties are grouped together as Literary Arabic (fuṣḥā), which is the official language of 26 states and the liturgical language of Islam. Modern Standard Arabic largely follows the grammatical standards of Classical Arabic and uses much of the same vocabulary. However, it has discarded some grammatical constructions and vocabulary that no longer have any counterpart in the spoken varieties, and has adopted certain new constructions and vocabulary from the spoken varieties. Much of the new vocabulary is used to denote concepts that have arisen in the post-classical era, especially in modern times. During the Middle Ages, Literary Arabic was a major vehicle of culture in Europe, especially in science, mathematics and philosophy. As a result, many European languages have also borrowed many words from it. Arabic influence, mainly in vocabulary, is seen in European languages, mainly Spanish and to a lesser extent Portuguese, Valencian and Catalan, owing to both the proximity of Christian European and Muslim Arab civilizations and 800 years of Arabic culture and language in the Iberian Peninsula, referred to in Arabic as al-Andalus. Sicilian has about 500 Arabic words as result of Sicily being progressively conquered by Arabs from North Africa, from the mid 9th to mid 10th centuries. Many of these words relate to agriculture and related activities (Hull and Ruffino). Balkan languages, including Greek and Bulgarian, have also acquired a significant number of Arabic words through contact with Ottoman Turkish. Arabic has influenced many languages around the globe throughout its history. Some of the most influenced languages are Persian, Turkish, Spanish, Urdu, Kashmiri, Kurdish, Bosnian, Kazakh, Bengali, Hindi, Malay, Maldivian, Indonesian, Pashto, Punjabi, Tagalog, Sindhi, and Hausa, and some languages in parts of Africa. Conversely, Arabic has borrowed words from other languages, including Greek and Persian in medieval times, and contemporary European languages such as English and French in modern times. Classical Arabic is the liturgical language of 1.8 billion Muslims and Modern Standard Arabic is one of six official languages of the United Nations. All varieties of Arabic combined are spoken by perhaps as many as 422 million speakers (native and non-native) in the Arab world, making it the fifth most spoken language in the world. Arabic is written with the Arabic alphabet, which is an abjad script and is written from right to left, although the spoken varieties are sometimes written in ASCII Latin from left to right with no standardized orthography.
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Aryabhatiya
Aryabhatiya (IAST) or Aryabhatiyam, a Sanskrit astronomical treatise, is the magnum opus and only known surviving work of the 5th century Indian mathematician Aryabhata.
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Āryabhaṭa's sine table
Āryabhaṭa's sine table is a set of twenty-four numbers given in the astronomical treatise Āryabhaṭīya composed by the fifth century Indian mathematician and astronomer Āryabhaṭa (476–550 CE), for the computation of the half-chords of certain set of arcs of a circle.
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İznik
İznik is a town and an administrative district in the Province of Bursa, Turkey.
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Bantam Books
Bantam Books is an American publishing house owned entirely by parent company Random House, a subsidiary of Penguin Random House; it is an imprint of the Random House Publishing Group.
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Bhaskara I's sine approximation formula
In mathematics, Bhaskara I's sine approximation formula is a rational expression in one variable for the computation of the approximate values of the trigonometric sines discovered by Bhaskara I (c. 600 – c. 680), a seventh-century Indian mathematician.
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C (programming language)
C (as in the letter ''c'') is a general-purpose, imperative computer programming language, supporting structured programming, lexical variable scope and recursion, while a static type system prevents many unintended operations.
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C mathematical functions
C mathematical operations are a group of functions in the standard library of the C programming language implementing basic mathematical functions.
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C standard library
The C standard library or libc is the standard library for the C programming language, as specified in the ANSI C standard.
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Cartesian coordinate system
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.
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Chord (geometry)
A chord of a circle is a straight line segment whose endpoints both lie on the circle.
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Circumscribed circle
In geometry, the circumscribed circle or circumcircle of a polygon is a circle which passes through all the vertices of the polygon.
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Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.
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Complex number
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
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Constant of integration
In calculus, the indefinite integral of a given function (i.e., the set of all antiderivatives of the function) on a connected domain is only defined up to an additive constant, the constant of integration.
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Convex function
In mathematics, a real-valued function defined on an ''n''-dimensional interval is called convex (or convex downward or concave upward) if the line segment between any two points on the graph of the function lies above or on the graph, in a Euclidean space (or more generally a vector space) of at least two dimensions.
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CORDIC
CORDIC (for COordinate Rotation DIgital Computer), also known as Volder's algorithm, is a simple and efficient algorithm to calculate hyperbolic and trigonometric functions, typically converging with one digit (or bit) per iteration.
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CPython
CPython is the reference implementation of the Python programming language.
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Data type
In computer science and computer programming, a data type or simply type is a classification of data which tells the compiler or interpreter how the programmer intends to use the data.
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Degree (angle)
A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle, defined so that a full rotation is 360 degrees.
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Derivative
The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).
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Differential equation
A differential equation is a mathematical equation that relates some function with its derivatives.
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Discrete sine transform
In mathematics, the discrete sine transform (DST) is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using a purely real matrix.
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Double-precision floating-point format
Double-precision floating-point format is a computer number format, usually occupying 64 bits in computer memory; it represents a wide dynamic range of numeric values by using a floating radix point.
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Egypt (Roman province)
The Roman province of Egypt (Aigyptos) was established in 30 BC after Octavian (the future emperor Augustus) defeated his rival Mark Antony, deposed Queen Cleopatra VII, and annexed the Ptolemaic Kingdom of Egypt to the Roman Empire.
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Entire function
In complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic at all finite points over the whole complex plane.
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Etymology
EtymologyThe New Oxford Dictionary of English (1998) – p. 633 "Etymology /ˌɛtɪˈmɒlədʒi/ the study of the class in words and the way their meanings have changed throughout time".
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Euler's continued fraction formula
In the analytic theory of continued fractions, Euler's continued fraction formula is an identity connecting a certain very general infinite series with an infinite continued fraction.
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Euler's formula
Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function.
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Exponential function
In mathematics, an exponential function is a function of the form in which the argument occurs as an exponent.
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Fixed point (mathematics)
In mathematics, a fixed point (sometimes shortened to fixpoint, also known as an invariant point) of a function is an element of the function's domain that is mapped to itself by the function.
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Floating-point arithmetic
In computing, floating-point arithmetic is arithmetic using formulaic representation of real numbers as an approximation so as to support a trade-off between range and precision.
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Fourier series
In mathematics, a Fourier series is a way to represent a function as the sum of simple sine waves.
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Functional equation
In mathematics, a functional equation is any equation in which the unknown represents a function.
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Gamma function
In mathematics, the gamma function (represented by, the capital Greek alphabet letter gamma) is an extension of the factorial function, with its argument shifted down by 1, to real and complex numbers.
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Generalized continued fraction
In complex analysis, a branch of mathematics, a generalized continued fraction is a generalization of regular continued fractions in canonical form, in which the partial numerators and partial denominators can assume arbitrary real or complex values.
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Generalized trigonometry
Ordinary trigonometry studies triangles in the Euclidean plane R2.
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Georg Joachim Rheticus
Georg Joachim de Porris, also known as Rheticus (16 February 1514 – 4 December 1574), was a mathematician, astronomer, cartographer, navigational-instrument maker, medical practitioner, and teacher.
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Gerard of Cremona
Gerard of Cremona (Latin: Gerardus Cremonensis; c. 1114 – 1187) was an Italian translator of scientific books from Arabic into Latin.
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Gottfried Wilhelm Leibniz
Gottfried Wilhelm (von) Leibniz (or; Leibnitz; – 14 November 1716) was a German polymath and philosopher who occupies a prominent place in the history of mathematics and the history of philosophy.
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Gradian
The gradian is a unit of measurement of an angle, equivalent to \frac of a turn, \frac of a degree, or \frac of a radian.
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Gregory's series
Gregory's series, also known as the Madhava–Gregory series or Leibniz's series, is an infinite Taylor series expansion of the inverse tangent function.
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Gupta Empire
The Gupta Empire was an ancient Indian empire, existing from approximately 240 to 590 CE.
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Hipparchus
Hipparchus of Nicaea (Ἵππαρχος, Hipparkhos) was a Greek astronomer, geographer, and mathematician.
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Holomorphic function
In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighborhood of every point in its domain.
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Hyperbolic function
In mathematics, hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions.
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Hypotenuse
In geometry, a hypotenuse (rarely: hypothenuse) is the longest side of a right-angled triangle, the side opposite of the right angle.
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Identity function
Graph of the identity function on the real numbers In mathematics, an identity function, also called an identity relation or identity map or identity transformation, is a function that always returns the same value that was used as its argument.
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IEEE 754 revision
IEEE 754-2008 (previously known as IEEE 754r) was published in August 2008 and is a significant revision to, and replaces, the IEEE 754-1985 floating point standard.
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Imaginary unit
The imaginary unit or unit imaginary number is a solution to the quadratic equation.
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Indian astronomy
Indian astronomy has a long history stretching from pre-historic to modern times.
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Inflection point
In differential calculus, an inflection point, point of inflection, flex, or inflection (British English: inflexion) is a point on a continuously differentiable plane curve at which the curve crosses its tangent, that is, the curve changes from being concave (concave downward) to convex (concave upward), or vice versa.
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Injective function
In mathematics, an injective function or injection or one-to-one function is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain.
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Integer
An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").
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Inverse function
In mathematics, an inverse function (or anti-function) is a function that "reverses" another function: if the function applied to an input gives a result of, then applying its inverse function to gives the result, and vice versa.
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Inverse trigonometric functions
In mathematics, the inverse trigonometric functions (occasionally also called arcus functions, antitrigonometric functions or cyclometric functions) are the inverse functions of the trigonometric functions (with suitably restricted domains).
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Irrational number
In mathematics, the irrational numbers are all the real numbers which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of integers.
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Jyā, koti-jyā and utkrama-jyā
Jyā, koti-jyā and utkrama-jyā are three trigonometric functions introduced by Indian mathematicians and astronomers.
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Laplace's equation
In mathematics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace who first studied its properties.
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Latin
Latin (Latin: lingua latīna) is a classical language belonging to the Italic branch of the Indo-European languages.
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Law of sines
In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of a triangle (any shape) to the sines of its angles.
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Legendre form
In mathematics, the Legendre forms of elliptic integrals are a canonical set of three elliptic integrals to which all others may be reduced.
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Leonhard Euler
Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.
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Limit of a function
Although the function (sin x)/x is not defined at zero, as x becomes closer and closer to zero, (sin x)/x becomes arbitrarily close to 1.
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List of periodic functions
This is a list of some well-known periodic functions.
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List of trigonometric identities
In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables where both sides of the equality are defined.
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Long double
In C and related programming languages, long double refers to a floating-point data type that is often more precise than double-precision.
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Madhava series
In mathematics, a Leibniz or Madhava series is any one of the series in a collection of infinite series expressions all of which are believed to have been discovered by Madhava of Sangamagrama (c. 1350 – c. 1425), the founder of the Kerala school of astronomy and mathematics and later by Gottfried Wilhelm Leibniz, among others.
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Madhava's sine table
Madhava's sine table is the table of trigonometric sines of various angles constructed by the 14th century Kerala mathematician-astronomer Madhava of Sangamagrama.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Maxima and minima
In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the local or relative extrema) or on the entire domain of a function (the global or absolute extrema).
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Medieval Latin
Medieval Latin was the form of Latin used in the Middle Ages, primarily as a medium of scholarly exchange, as the liturgical language of Chalcedonian Christianity and the Roman Catholic Church, and as a language of science, literature, law, and administration.
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Merriam-Webster
Merriam–Webster, Incorporated is an American company that publishes reference books which is especially known for its dictionaries.
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Monotonic function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.
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Multiplicative inverse
In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1.
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Nicolaus Copernicus
Nicolaus Copernicus (Mikołaj Kopernik; Nikolaus Kopernikus; Niklas Koppernigk; 19 February 1473 – 24 May 1543) was a Renaissance-era mathematician and astronomer who formulated a model of the universe that placed the Sun rather than the Earth at the center of the universe, likely independently of Aristarchus of Samos, who had formulated such a model some eighteen centuries earlier.
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Optical sine theorem
In optics, the optical sine theorem states that the products of the index, height, and sine of the slope angle of a ray in object space and its corresponding ray in image space are equal.
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Periodic function
In mathematics, a periodic function is a function that repeats its values in regular intervals or periods.
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Polar coordinate system
In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.
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Polar sine
In geometry, the polar sine generalizes the sine function of angle to the vertex angle of a polytope.
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Principal branch
In mathematics, a principal branch is a function which selects one branch ("slice") of a multi-valued function.
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Principal value
In complex analysis, the principal values of a multivalued function are the values along one chosen branch of that function, so that it is single-valued.
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Proofs of trigonometric identities
The main trigonometric identities between trigonometric functions are proved, using mainly the geometry of the right triangle.
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Ptolemy
Claudius Ptolemy (Κλαύδιος Πτολεμαῖος, Klaúdios Ptolemaîos; Claudius Ptolemaeus) was a Greco-Roman mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology.
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Pythagorean trigonometric identity
The Pythagorean trigonometric identity is a trigonometric identity expressing the Pythagorean theorem in terms of trigonometric functions.
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Python (programming language)
Python is an interpreted high-level programming language for general-purpose programming.
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Radian
The radian (SI symbol rad) is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics.
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Rational number
In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Riemann zeta function
The Riemann zeta function or Euler–Riemann zeta function,, is a function of a complex variable s that analytically continues the sum of the Dirichlet series which converges when the real part of is greater than 1.
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Right triangle
A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle).
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Roger Cotes
Roger Cotes FRS (10 July 1682 – 5 June 1716) was an English mathematician, known for working closely with Isaac Newton by proofreading the second edition of his famous book, the Principia, before publication.
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Sanskrit
Sanskrit is the primary liturgical language of Hinduism; a philosophical language of Hinduism, Sikhism, Buddhism and Jainism; and a former literary language and lingua franca for the educated of ancient and medieval India.
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Series (mathematics)
In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity.
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Sign (mathematics)
In mathematics, the concept of sign originates from the property of every non-zero real number of being positive or negative.
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Sign function
In mathematics, the sign function or signum function (from signum, Latin for "sign") is an odd mathematical function that extracts the sign of a real number.
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Similarity (geometry)
Two geometrical objects are called similar if they both have the same shape, or one has the same shape as the mirror image of the other.
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Sinc function
In mathematics, physics and engineering, the cardinal sine function or sinc function, denoted by, has two slightly different definitions.
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Sine and cosine transforms
In mathematics, the Fourier sine and cosine transforms are forms of the Fourier integral transform that do not use complex numbers.
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Sine quadrant
Sinecal Quadrant or as it is known in Arabic: Rub‘ul mujayyab The sine quadrant (Arabic: Rub‘ul mujayyab, الربع المجيب) was a type of quadrant used by medieval Arabic astronomers.
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Sine wave
A sine wave or sinusoid is a mathematical curve that describes a smooth periodic oscillation.
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Sine-Gordon equation
The sine-Gordon equation is a nonlinear hyperbolic partial differential equation in 1 + 1 dimensions involving the d'Alembert operator and the sine of the unknown function.
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Single-precision floating-point format
Single-precision floating-point format is a computer number format, usually occupying 32 bits in computer memory; it represents a wide dynamic range of numeric values by using a floating radix point.
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Sinusoidal model
In statistics, signal processing, and time series analysis, a sinusoidal model to approximate a sequence Yi is: where C is constant defining a mean level, α is an amplitude for the sine wave, ω is the frequency, Ti is a time variable, φ is the phase, and Ei is the error sequence in approximating the sequence Yi by the model.
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Sound
In physics, sound is a vibration that typically propagates as an audible wave of pressure, through a transmission medium such as a gas, liquid or solid.
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Surya Siddhanta
The Surya Siddhanta is the name of a Sanskrit treatise in Indian astronomy from 6th Century BCE.
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Taylor series
In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.
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Transliteration
Transliteration is a type of conversion of a text from one script to another that involves swapping letters (thus trans- + liter-) in predictable ways (such as α → a, д → d, χ → ch, ն → n or æ → e).
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Triangle
A triangle is a polygon with three edges and three vertices.
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Triangulation
In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to it from known points.
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Trigonometric functions
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle.
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Trigonometric integral
In mathematics, the trigonometric integrals are a family of integrals involving trigonometric functions.
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Trigonometry
Trigonometry (from Greek trigōnon, "triangle" and metron, "measure") is a branch of mathematics that studies relationships involving lengths and angles of triangles.
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Turn (geometry)
A turn is a unit of plane angle measurement equal to 2pi radians, 360 degrees or 400 gradians.
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Unit circle
In mathematics, a unit circle is a circle with a radius of one.
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Uta Merzbach
Uta Caecilia Merzbach (February 9, 1933 – June 27, 2017) was a German-American historian of mathematics who became the first curator of mathematical instruments at the Smithsonian Institution.
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Zero of a function
In mathematics, a zero, also sometimes called a root, of a real-, complex- or generally vector-valued function f is a member x of the domain of f such that f(x) vanishes at x; that is, x is a solution of the equation f(x).
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Complex sine, Half chord, Half-chord, Natural sine, Sin (trigonometry), Sin x, Sin z, Sin(), Sin(x), Sine (mathematics), Sine (trigonometric function), Sine (trigonometry), Sine function, Sinus (trigonometry), Sinus rectus (function), Sinus rectus (mathematics), Sinus rectus (trigonometry), Sinus rectus arcus, Sinus rectus primus, Sinusoida, Vertical sine.
References
[1] https://en.wikipedia.org/wiki/Sine
