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133 relations: Abramowitz and Stegun, Absolute convergence, Alexandroff extension, Alpha, American Mathematical Monthly, Angle, Angle trisection, Antiderivative, Arc length, Association for Computing Machinery, Atan2, Barnes & Noble, Beat (acoustics), Bessel function, Beta, Binomial coefficient, Binomial theorem, Butterworth filter, Calculus, Casus irreducibilis, Charles Hermite, Chebyshev polynomials, Chord (geometry), Cis (mathematics), Cofiniteness, Compass-and-straightedge construction, Complex number, Convolution, Coprime integers, Cube root, Cubic function, Curve fitting, Cyclotomic polynomial, De Moivre's formula, Degree (angle), Derivative, Differential equation, Dirichlet kernel, Discriminant, Distribution (mathematics), Dover Publications, Elementary symmetric polynomial, Empty product, Euclid, Euclid's Elements, Euler's formula, Euler's identity, Even and odd functions, Exsecant, Field (mathematics), ..., Fourier transform, François Viète, Gamma, Golden ratio, Gradian, Greek alphabet, Group representation, Gudermannian function, Half-side formula, Haversine formula, Hyperbolic function, Hypotenuse, Identity (mathematics), Imaginary unit, In-phase and quadrature components, Infinite product, Integral, Inverse function, Inverse trigonometric functions, Invertible matrix, Jacobian matrix and determinant, John Machin, Jordan measure, Joseph-Louis Lagrange, Law of cosines, Law of cotangents, Law of sines, Law of tangents, Leonhard Euler, Linear combination, List of integrals of trigonometric functions, List of trigonometric identities, Mathematical induction, Mathematics, Matrix (mathematics), Möbius function, Möbius transformation, Measure (mathematics), Medical imaging, Mnemonics in trigonometry, Mollweide's formula, Morrie's law, Niven's theorem, Orthogonal group, Pafnuty Chebyshev, Phase (waves), Phase detector, Pi, Prime number, Proofs of trigonometric identities, Prosthaphaeresis, Ptolemy, Ptolemy's table of chords, Pythagorean theorem, Pythagorean triple, Radian, Ratio, Rational trigonometry, Real number, Right triangle, SIGSAM, Sinc function, Sine, Sine wave, Special functions, Spherical law of cosines, Squeeze theorem, Standing wave, Tangent half-angle formula, Taylor series, Theta, Transpose, Triangle, Trigonometric constants expressed in real radicals, Trigonometric functions, Trigonometric substitution, Trigonometry, Turn (geometry), Unit circle, Up to, Uses of trigonometry, Variable (mathematics), Versine. Expand index (83 more) »
Abramowitz and Stegun
Abramowitz and Stegun (AS) is the informal name of a mathematical reference work edited by Milton Abramowitz and Irene Stegun of the United States National Bureau of Standards (NBS), now the National Institute of Standards and Technology (NIST).
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Absolute convergence
In mathematics, an infinite series of numbers is said to converge absolutely (or to be absolutely convergent) if the sum of the absolute values of the summands is finite.
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Alexandroff extension
In the mathematical field of topology, the Alexandroff extension is a way to extend a noncompact topological space by adjoining a single point in such a way that the resulting space is compact.
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Alpha
Alpha (uppercase, lowercase; ἄλφα, álpha, modern pronunciation álfa) is the first letter of the Greek alphabet.
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American Mathematical Monthly
The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894.
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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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Angle trisection
Angle trisection is a classical problem of compass and straightedge constructions of ancient Greek mathematics.
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Antiderivative
In calculus, an antiderivative, primitive function, primitive integral or indefinite integral of a function is a differentiable function whose derivative is equal to the original function.
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Arc length
Determining the length of an irregular arc segment is also called rectification of a curve.
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Association for Computing Machinery
The Association for Computing Machinery (ACM) is an international learned society for computing.
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Atan2
The function \operatorname (y,x) or \operatorname (y,x) is defined as the angle in the Euclidean plane, given in rad, between the positive x-axis and the ray to the Points in the upper half-plane deliver values in points with.
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Barnes & Noble
Barnes & Noble, Inc., a Fortune 500 company, is the bookseller with the largest number of retail outlets in the United States, and a retailer of content, digital media, and educational products.
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Beat (acoustics)
In acoustics, a beat is an interference pattern between two sounds of slightly different frequencies, perceived as a periodic variation in volume whose rate is the difference of the two frequencies.
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Bessel function
Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are the canonical solutions of Bessel's differential equation for an arbitrary complex number, the order of the Bessel function.
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Beta
Beta (uppercase, lowercase, or cursive; bē̂ta or βήτα) is the second letter of the Greek alphabet.
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Binomial coefficient
In mathematics, any of the positive integers that occurs as a coefficient in the binomial theorem is a binomial coefficient.
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Binomial theorem
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.
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Butterworth filter
The Butterworth filter is a type of signal processing filter designed to have a frequency response as flat as possible in the passband.
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Calculus
Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus), is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.
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Casus irreducibilis
In algebra, casus irreducibilis (Latin for "the irreducible case") is one of the cases that may arise in attempting to solve a cubic equation with integer coefficients with roots that are expressed with radicals.
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Charles Hermite
Prof Charles Hermite FRS FRSE MIAS (24 December 1822 – 14 January 1901) was a French mathematician who did research concerning number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra.
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Chebyshev polynomials
In mathematics the Chebyshev polynomials, named after Pafnuty Chebyshev, are a sequence of orthogonal polynomials which are related to de Moivre's formula and which can be defined recursively.
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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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Cis (mathematics)
is a less commonly used mathematical notation defined by, where is the cosine function, is the imaginary unit and is the sine.
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Cofiniteness
In mathematics, a cofinite subset of a set X is a subset A whose complement in X is a finite set.
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Compass-and-straightedge construction
Compass-and-straightedge construction, also known as ruler-and-compass construction or classical construction, is the construction of lengths, angles, and other geometric figures using only an idealized ruler and compass.
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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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Convolution
In mathematics (and, in particular, functional analysis) convolution is a mathematical operation on two functions (f and g) to produce a third function, that is typically viewed as a modified version of one of the original functions, giving the integral of the pointwise multiplication of the two functions as a function of the amount that one of the original functions is translated.
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Coprime integers
In number theory, two integers and are said to be relatively prime, mutually prime, or coprime (also written co-prime) if the only positive integer (factor) that divides both of them is 1.
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Cube root
In mathematics, a cube root of a number x is a number y such that y3.
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Cubic function
In algebra, a cubic function is a function of the form in which is nonzero.
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Curve fitting
Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints.
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Cyclotomic polynomial
In mathematics, more specifically in algebra, the nth cyclotomic polynomial, for any positive integer n, is the unique irreducible polynomial with integer coefficients that is a divisor of x^n-1 and is not a divisor of x^k-1 for any.
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De Moivre's formula
In mathematics, de Moivre's formula (also known as de Moivre's theorem and de Moivre's identity), named after Abraham de Moivre, states that for any complex number (and, in particular, for any real number) and integer it holds that where is the imaginary unit.
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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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Dirichlet kernel
In mathematical analysis, the Dirichlet kernel is the collection of functions e^.
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Discriminant
In algebra, the discriminant of a polynomial is a polynomial function of its coefficients, which allows deducing some properties of the roots without computing them.
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Distribution (mathematics)
Distributions (or generalized functions) are objects that generalize the classical notion of functions in mathematical analysis.
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Dover Publications
Dover Publications, also known as Dover Books, is an American book publisher founded in 1941 by Hayward Cirker and his wife, Blanche.
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Elementary symmetric polynomial
In mathematics, specifically in commutative algebra, the elementary symmetric polynomials are one type of basic building block for symmetric polynomials, in the sense that any symmetric polynomial can be expressed as a polynomial in elementary symmetric polynomials.
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Empty product
In mathematics, an empty product, or nullary product, is the result of multiplying no factors.
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Euclid
Euclid (Εὐκλείδης Eukleidēs; fl. 300 BC), sometimes given the name Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry".
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Euclid's Elements
The Elements (Στοιχεῖα Stoicheia) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC.
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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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Euler's identity
In mathematics, Euler's identity (also known as Euler's equation) is the equality where Euler's identity is named after the Swiss mathematician Leonhard Euler.
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Even and odd functions
In mathematics, even functions and odd functions are functions which satisfy particular symmetry relations, with respect to taking additive inverses.
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Exsecant
The exsecant (exsec, exs) and excosecant (excosec, excsc, exc) are trigonometric functions defined in terms of the secant and cosecant functions.
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Field (mathematics)
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.
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Fourier transform
The Fourier transform (FT) decomposes a function of time (a signal) into the frequencies that make it up, in a way similar to how a musical chord can be expressed as the frequencies (or pitches) of its constituent notes.
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François Viète
François Viète (Franciscus Vieta; 1540 – 23 February 1603), Seigneur de la Bigotière, was a French mathematician whose work on new algebra was an important step towards modern algebra, due to its innovative use of letters as parameters in equations.
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Gamma
Gamma (uppercase, lowercase; gámma) is the third letter of the Greek alphabet.
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Golden ratio
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.
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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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Greek alphabet
The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BC.
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Group representation
In the mathematical field of representation theory, group representations describe abstract groups in terms of linear transformations of vector spaces; in particular, they can be used to represent group elements as matrices so that the group operation can be represented by matrix multiplication.
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Gudermannian function
The Gudermannian function, named after Christoph Gudermann (1798–1852), relates the circular functions and hyperbolic functions without explicitly using complex numbers.
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Half-side formula
In spherical trigonometry, the half side formula relates the angles and lengths of the sides of spherical triangles, which are triangles drawn on the surface of a sphere and so have curved sides and do not obey the formulas for plane triangles.
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Haversine formula
The haversine formula determines the great-circle distance between two points on a sphere given their longitudes and latitudes.
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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 (mathematics)
In mathematics an identity is an equality relation A.
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Imaginary unit
The imaginary unit or unit imaginary number is a solution to the quadratic equation.
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In-phase and quadrature components
In electrical engineering, a sinusoid with angle modulation can be decomposed into, or synthesized from, two amplitude-modulated sinusoids that are offset in phase by one-quarter cycle (/2 radians).
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Infinite product
In mathematics, for a sequence of complex numbers a1, a2, a3,...
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Integral
In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.
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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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Invertible matrix
In linear algebra, an n-by-n square matrix A is called invertible (also nonsingular or nondegenerate) if there exists an n-by-n square matrix B such that where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication.
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Jacobian matrix and determinant
In vector calculus, the Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function.
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John Machin
John Machin (bapt. c. 1686 – June 9, 1751), a professor of astronomy at Gresham College, London, is best known for developing a quickly converging series for Pi in 1706 and using it to compute Pi to 100 decimal places.
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Jordan measure
In mathematics, the Peano–Jordan measure (also known as the Jordan content) is an extension of the notion of size (length, area, volume) to shapes more complicated than, for example, a triangle, disk, or parallelepiped.
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Joseph-Louis Lagrange
Joseph-Louis Lagrange (or;; born Giuseppe Lodovico Lagrangia, Encyclopædia Britannica or Giuseppe Ludovico De la Grange Tournier, Turin, 25 January 1736 – Paris, 10 April 1813; also reported as Giuseppe Luigi Lagrange or Lagrangia) was an Italian Enlightenment Era mathematician and astronomer.
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Law of cosines
In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles.
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Law of cotangents
In trigonometry, the law of cotangents is a relationship among the lengths of the sides of a triangle and the cotangents of the halves of the three angles.
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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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Law of tangents
In trigonometry, the law of tangents is a statement about the relationship between the tangents of two angles of a triangle and the lengths of the opposing sides.
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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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Linear combination
In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants).
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List of integrals of trigonometric functions
The following is a list of integrals (antiderivative functions) of trigonometric 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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Mathematical induction
Mathematical induction is a mathematical proof technique.
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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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Matrix (mathematics)
In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.
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Möbius function
The classical Möbius function is an important multiplicative function in number theory and combinatorics.
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Möbius transformation
In geometry and complex analysis, a Möbius transformation of the complex plane is a rational function of the form of one complex variable z; here the coefficients a, b, c, d are complex numbers satisfying ad − bc ≠ 0.
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Measure (mathematics)
In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size.
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Medical imaging
Medical imaging is the technique and process of creating visual representations of the interior of a body for clinical analysis and medical intervention, as well as visual representation of the function of some organs or tissues (physiology).
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Mnemonics in trigonometry
In trigonometry, it is common to use mnemonics to help remember trigonometric identities and the relationships between the various trigonometric functions.
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Mollweide's formula
In trigonometry, Mollweide's formula, sometimes referred to in older texts as Mollweide's equations, named after Karl Mollweide, is a set of two relationships between sides and angles in a triangle.
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Morrie's law
Morrie's law is the trigonometric identity It is a special case of the more general identity with n.
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Niven's theorem
In mathematics, Niven's theorem, named after Ivan Niven, states that the only rational values of θ in the interval 0° ≤ θ ≤ 90° for which the sine of θ degrees is also a rational number are: \begin \sin 0^\circ &.
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Orthogonal group
In mathematics, the orthogonal group in dimension, denoted, is the group of distance-preserving transformations of a Euclidean space of dimension that preserve a fixed point, where the group operation is given by composing transformations.
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Pafnuty Chebyshev
Pafnuty Lvovich Chebyshev (p) (–) was a Russian mathematician.
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Phase (waves)
Phase is the position of a point in time (an instant) on a waveform cycle.
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Phase detector
A phase detector or phase comparator is a frequency mixer, analog multiplier or logic circuit that generates a voltage signal which represents the difference in phase between two signal inputs.
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Pi
The number is a mathematical constant.
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Prime number
A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.
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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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Prosthaphaeresis
Prosthaphaeresis (from the Greek προσθαφαίρεσις) was an algorithm used in the late 16th century and early 17th century for approximate multiplication and division using formulas from trigonometry.
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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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Ptolemy's table of chords
The table of chords, created by the astronomer, geometer, and geographer Ptolemy in Egypt during the 2nd century AD, is a trigonometric table in Book I, chapter 11 of Ptolemy's Almagest, a treatise on mathematical astronomy.
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Pythagorean theorem
In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle.
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Pythagorean triple
A Pythagorean triple consists of three positive integers,, and, such that.
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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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Ratio
In mathematics, a ratio is a relationship between two numbers indicating how many times the first number contains the second.
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Rational trigonometry
Rational trigonometry is a proposed reformulation of metrical planar and solid geometries (which includes trigonometry) by Canadian mathematician Norman J. Wildberger, currently an associate professor of mathematics at the University of New South Wales.
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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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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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SIGSAM
SIGSAM is the ACM Special Interest Group on Symbolic and Algebraic Manipulation.
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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
In mathematics, the sine is a trigonometric function of an angle.
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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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Special functions
Special functions are particular mathematical functions which have more or less established names and notations due to their importance in mathematical analysis, functional analysis, physics, or other applications.
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Spherical law of cosines
In spherical trigonometry, the law of cosines (also called the cosine rule for sides) is a theorem relating the sides and angles of spherical triangles, analogous to the ordinary law of cosines from plane trigonometry.
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Squeeze theorem
In calculus, the squeeze theorem, also known as the pinching theorem, the sandwich theorem, the sandwich rule, and sometimes the squeeze lemma, is a theorem regarding the limit of a function.
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Standing wave
In physics, a standing wave – also known as a stationary wave – is a wave which oscillates in time but whose peak amplitude profile does not move in space.
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Tangent half-angle formula
In trigonometry, tangent half-angle formulas relate the tangent of half of an angle to trigonometric functions of the entire angle.
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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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Theta
Theta (uppercase Θ or ϴ, lowercase θ (which resembles digit 0 with horizontal line) or ϑ; θῆτα thē̂ta; Modern: θήτα| thī́ta) is the eighth letter of the Greek alphabet, derived from the Phoenician letter Teth.
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Transpose
In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal, that is it switches the row and column indices of the matrix by producing another matrix denoted as AT (also written A′, Atr, tA or At).
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Triangle
A triangle is a polygon with three edges and three vertices.
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Trigonometric constants expressed in real radicals
Exact algebraic expressions for trigonometric values are sometimes useful, mainly for simplifying solutions into radical forms which allow further simplification.
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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 substitution
In mathematics, Trigonometric substitution is the substitution of trigonometric functions for other expressions.
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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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Up to
In mathematics, the phrase up to appears in discussions about the elements of a set (say S), and the conditions under which subsets of those elements may be considered equivalent.
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Uses of trigonometry
Amongst the lay public of non-mathematicians and non-scientists, trigonometry is known chiefly for its application to measurement problems, yet is also often used in ways that are far more subtle, such as its place in the theory of music; still other uses are more technical, such as in number theory.
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Variable (mathematics)
In elementary mathematics, a variable is a symbol, commonly an alphabetic character, that represents a number, called the value of the variable, which is either arbitrary, not fully specified, or unknown.
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Versine
The versine or versed sine is a trigonometric function already appearing in some of the earliest trigonometric tables.
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References
[1] https://en.wikipedia.org/wiki/List_of_trigonometric_identities
