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Inverse trigonometric functions, the Glossary

87 relations: A K Peters, Absolute value, Analytic function, Arcsine distribution, Argument (complex analysis), Atan2, Binomial series, Bookboon, Branch point, C (programming language), Cambridge University Press, Carl Friedrich Gauss, Circular arc, Complex logarithm, Complex number, Complex plane, Condition number, Countable set, Degree (angle), Derivative, Domain coloring, Domain of a function, Dover Publications, Empty product, Engineering, Euler's formula, Exsecant, Generalized continued fraction, Geometric series, Geometry, Henry Holt and Company, Hyperbolic angle, Hypergeometric function, If and only if, Imaginary unit, Improper integral, Injective function, Integer, Integration by parts, Integration by substitution, International Organization for Standardization, Inverse function, Inverse hyperbolic functions, Inverse trigonometric functions, John Herschel, Lahore, Leibniz formula for π, Leonhard Euler, Letter case, List of integrals of inverse trigonometric functions, ... Expand index (37 more) »
Elementary special functions
Mathematical relations

A K Peters

A K Peters, Ltd. was a publisher of scientific and technical books, specializing in mathematics and in computer graphics, robotics, and other fields of computer science.

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Absolute value

In mathematics, the absolute value or modulus of a real number x, is the non-negative value without regard to its sign.

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Analytic function

In mathematics, an analytic function is a function that is locally given by a convergent power series.

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In probability theory, the arcsine distribution is the probability distribution whose cumulative distribution function involves the arcsine and the square root: for 0 ≤ x ≤ 1, and whose probability density function is on (0, 1).

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Argument (complex analysis)

In mathematics (particularly in complex analysis), the argument of a complex number, denoted, is the angle between the positive real axis and the line joining the origin and, represented as a point in the complex plane, shown as \varphi in Figure 1. Inverse trigonometric functions and argument (complex analysis) are trigonometry.

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Atan2

In computing and mathematics, the function atan2 is the 2-argument arctangent.

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Binomial series

In mathematics, the binomial series is a generalization of the polynomial that comes from a binomial formula expression like (1+x)^n for a nonnegative integer n. Specifically, the binomial series is the MacLaurin series for the function f(x).

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Bookboon

Bookboon Learning is a digital learning service provider for corporate learning & development, providing eBooks, audio learning, online courses & learning.

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Branch point

In the mathematical field of complex analysis, a branch point of a multivalued function is a point such that if the function is n-valued (has n values) at that point, all of its neighborhoods contain a point that has more than n values.

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C (programming language)

C (pronounced – like the letter c) is a general-purpose programming language.

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Cambridge University Press

Cambridge University Press is the university press of the University of Cambridge.

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Carl Friedrich Gauss

Johann Carl Friedrich Gauss (Gauß; Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician, astronomer, geodesist, and physicist who contributed to many fields in mathematics and science.

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Circular arc

A circular arc is the arc of a circle between a pair of distinct points.

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Complex logarithm

In mathematics, a complex logarithm is a generalization of the natural logarithm to nonzero complex numbers.

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Complex number

In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted, called the imaginary unit and satisfying the equation i^.

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Complex plane

In mathematics, the complex plane is the plane formed by the complex numbers, with a Cartesian coordinate system such that the horizontal -axis, called the real axis, is formed by the real numbers, and the vertical -axis, called the imaginary axis, is formed by the imaginary numbers.

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Condition number

In numerical analysis, the condition number of a function measures how much the output value of the function can change for a small change in the input argument.

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Countable set

In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers.

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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 in which one full rotation is 360 degrees.

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Derivative

The derivative is a fundamental tool of calculus that quantifies the sensitivity of change of a function's output with respect to its input.

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Domain coloring

In complex analysis, domain coloring or a color wheel graph is a technique for visualizing complex functions by assigning a color to each point of the complex plane.

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Domain of a function

In mathematics, the domain of a function is the set of inputs accepted by the function.

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Dover Publications

Dover Publications, also known as Dover Books, is an American book publisher founded in 1941 by Hayward and Blanche Cirker.

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Empty product

In mathematics, an empty product, or nullary product or vacuous product, is the result of multiplying no factors.

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Engineering

Engineering is the practice of using natural science, mathematics, and the engineering design process to solve technical problems, increase efficiency and productivity, and improve systems.

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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. Inverse trigonometric functions and Euler's formula are trigonometry.

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Exsecant

The external secant function (exsecant, symbolized exsec) is a trigonometric function defined in terms of the secant function: \operatorname \theta.

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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 complex values.

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Geometric series

In mathematics, a geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms. Inverse trigonometric functions and geometric series are ratios.

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Geometry

Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures.

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Henry Holt and Company

Henry Holt and Company is an American book-publishing company based in New York City.

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Hyperbolic angle

In geometry, hyperbolic angle is a real number determined by the area of the corresponding hyperbolic sector of xy.

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Hypergeometric function

In mathematics, the Gaussian or ordinary hypergeometric function 2F1(a,b;c;z) is a special function represented by the hypergeometric series, that includes many other special functions as specific or limiting cases.

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If and only if

In logic and related fields such as mathematics and philosophy, "if and only if" (often shortened as "iff") is paraphrased by the biconditional, a logical connective between statements.

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Imaginary unit

The imaginary unit or unit imaginary number is a solution to the quadratic equation Although there is no real number with this property, can be used to extend the real numbers to what are called complex numbers, using addition and multiplication.

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Improper integral

In mathematical analysis, an improper integral is an extension of the notion of a definite integral to cases that violate the usual assumptions for that kind of integral.

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Injective function

In mathematics, an injective function (also known as injection, or one-to-one function) is a function that maps distinct elements of its domain to distinct elements; that is, implies.

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Integer

An integer is the number zero (0), a positive natural number (1, 2, 3,...), or the negation of a positive natural number (−1, −2, −3,...). The negations or additive inverses of the positive natural numbers are referred to as negative integers.

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Integration by parts

In calculus, and more generally in mathematical analysis, integration by parts or partial integration is a process that finds the integral of a product of functions in terms of the integral of the product of their derivative and antiderivative.

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Integration by substitution

In calculus, integration by substitution, also known as u-substitution, reverse chain rule or change of variables, is a method for evaluating integrals and antiderivatives.

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International Organization for Standardization

The International Organization for Standardization (ISO) is an independent, non-governmental, international standard development organization composed of representatives from the national standards organizations of member countries.

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Inverse function

In mathematics, the inverse function of a function (also called the inverse of) is a function that undoes the operation of.

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Inverse hyperbolic functions

In mathematics, the inverse hyperbolic functions are inverses of the hyperbolic functions, analogous to the inverse circular functions. Inverse trigonometric functions and inverse hyperbolic functions are Elementary special functions.

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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). Inverse trigonometric functions and inverse trigonometric functions are Dimensionless numbers, Elementary special functions, mathematical relations, ratios and trigonometry.

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John Herschel

Sir John Frederick William Herschel, 1st Baronet (7 March 1792 – 11 May 1871) was an English polymath active as a mathematician, astronomer, chemist, inventor and experimental photographer who invented the blueprint and did botanical work.

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Lahore

Lahore (لہور; لاہور) is the capital and largest city of the Pakistani province of Punjab.

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Leibniz formula for π

In mathematics, the Leibniz formula for pi, named after Gottfried Wilhelm Leibniz, states that \frac.

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Leonhard Euler

Leonhard Euler (15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician, and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in many other branches of mathematics such as analytic number theory, complex analysis, and infinitesimal calculus.

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Letter case

Letter case is the distinction between the letters that are in larger uppercase or capitals (or more formally majuscule) and smaller lowercase (or more formally minuscule) in the written representation of certain languages.

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List of integrals of inverse trigonometric functions

The following is a list of indefinite integrals (antiderivatives) of expressions involving the inverse trigonometric functions.

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List of trigonometric identities

In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Inverse trigonometric functions and List of trigonometric identities are trigonometry.

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Logical equality

Logical equality is a logical operator that corresponds to equality in Boolean algebra and to the logical biconditional in propositional calculus.

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Macmillan Inc.

Macmillan Inc. was an American book publishing company originally established as the American division of the British Macmillan Publishers.

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Magma (computer algebra system)

Magma is a computer algebra system designed to solve problems in algebra, number theory, geometry and combinatorics.

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Maple (software)

Maple is a symbolic and numeric computing environment as well as a multi-paradigm programming language.

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Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

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MATLAB

MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks.

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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. Inverse trigonometric functions and multiplicative inverse are Elementary special functions.

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Multivalued function

In mathematics, a multivalued function (also known as a multiple-valued function) is a function that has two or more values in its range for at least one point in its domain.

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Navigation is a field of study that focuses on the process of monitoring and controlling the movement of a craft or vehicle from one place to another.

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Nuclear Instruments and Methods in Physics Research

Nuclear Instruments and Methods in Physics Research (Nucl. Instrum. Methods Phys. Res.) is a peer-reviewed scientific journal published by Elsevier.

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NumPy

NumPy (pronounced) is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays.

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Parity (mathematics)

In mathematics, parity is the property of an integer of whether it is even or odd.

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Physics

Physics is the natural science of matter, involving the study of matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force.

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Power series

In mathematics, a power series (in one variable) is an infinite series of the form \sum_^\infty a_n \left(x - c\right)^n.

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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 mathematics, specifically 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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Pythagorean theorem

In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.

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Python (programming language)

Python is a high-level, general-purpose programming language.

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Radian

The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics.

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Range of a function

In mathematics, the range of a function may refer to either of two closely related concepts.

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Right triangle

A right triangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular forming a right angle (turn or 90 degrees).

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Sign function

In mathematics, the sign function or signum function (from signum, Latin for "sign") is a function that has the value, or according to whether the sign of a given real number is positive or negative, or the given number is itself zero.

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Sine and cosine

In mathematics, sine and cosine are trigonometric functions of an angle.

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Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

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Square root

In mathematics, a square root of a number is a number such that y^2. Inverse trigonometric functions and square root are Elementary special functions.

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Subset

In mathematics, a set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B. The relationship of one set being a subset of another is called inclusion (or sometimes containment).

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SymPy

SymPy is an open-source Python library for symbolic computation.

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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. Inverse trigonometric functions and tangent half-angle formula are trigonometry.

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Taylor series

In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point.

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Trigonometric functions

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. Inverse trigonometric functions and trigonometric functions are Dimensionless numbers, Elementary special functions, ratios and trigonometry.

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Trigonometric functions of matrices

The trigonometric functions (especially sine and cosine) for real or complex square matrices occur in solutions of second-order systems of differential equations. Inverse trigonometric functions and trigonometric functions of matrices are trigonometry.

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Unit circle

In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. Inverse trigonometric functions and unit circle are trigonometry.

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University of Konstanz

The University of Konstanz (Universität Konstanz) is a university in the city of Konstanz in Baden-Württemberg, Germany.

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Versine

The versine or versed sine is a trigonometric function found in some of the earliest (Sanskrit ''Aryabhatia'', Section I) trigonometric tables.

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Well-defined expression

In mathematics, a well-defined expression or unambiguous expression is an expression whose definition assigns it a unique interpretation or value.

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Wolfram Mathematica

Wolfram Mathematica is a software system with built-in libraries for several areas of technical computing that allow machine learning, statistics, symbolic computation, data manipulation, network analysis, time series analysis, NLP, optimization, plotting functions and various types of data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other programming languages.

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References

[1] https://en.wikipedia.org/wiki/Inverse_trigonometric_functions

Also known as Acos (function), Anti-cosecant, Anti-cosine, Anti-cotangent, Anti-secant, Anti-sine, Anti-tangent, Anti-trigonometric function, Anti-trigonometric functions, Anticosecant, Anticosine, Anticotangent, Antisecant, Antisine, Antitangent, Antitrigonometric function, Antitrigonometric functions, Arc (function prefix), Arc Cosecant, Arc Cosine, Arc Cotangent, Arc Secant, Arc Sine, Arc Tangent, Arc function, Arc functions, Arc trigonometric function, Arc trigonometric functions, Arc- (function prefix), Arc-cosecant, Arc-cosine, Arc-cotangent, Arc-secant, Arc-sine, Arc-tangent, Arc-trigonometric function, Arc-trigonometric functions, ArcSin, Arccos (trigonometry), Arccos(x), Arccosec, Arccosecant, Arccosine, Arccosinus, Arccot, Arccot (trigonometry), Arccotangent, Arccsc, Arccsc (trigonometry), Arcctg, Arcctg (trigonometric function), Arcsec (function), Arcsec (trigonometric function), Arcsec (trigonometry), Arcsecant, Arcsin (trigonometry), Arcsin(x), Arcsine, Arcsinus, Arctan, Arctan (trigonometry), Arctan(x), Arctangent, Arctangent function, Arctg, Arctg (trigonometric function), Arcus cosecans, Arcus cosinus, Arcus cotangens, Arcus function, Arcus secans, Arcus sinus, Arcus tangens, Asec (function), Asin (function), Atan (function), Cyclometric, Cyclometric function, Cyclometric functions, Inv cos, Inv cot, Inv csc, Inv sec, Inv sin, Inv tan, Inverse circular function, Inverse circular functions, Inverse cosecant, Inverse cosine, Inverse cotangent, Inverse secant, Inverse sine, Inverse tangent, Inverse trig, Inverse trig function, Inverse trig functions, Inverse trigonometric, Inverse trigonometric cofunctions, Inverse trigonometric cosecant, Inverse trigonometric cosine, Inverse trigonometric cotangent, Inverse trigonometric function, Inverse trigonometric secant, Inverse trigonometric sine, Inverse trigonometric tangent, Inverse trigonometry, Trigonometric arcus function, Trigonometric arcus functions.

, List of trigonometric identities, Logical equality, Macmillan Inc., Magma (computer algebra system), Maple (software), Mathematics, MATLAB, Multiplicative inverse, Multivalued function, Navigation, Nuclear Instruments and Methods in Physics Research, NumPy, Parity (mathematics), Physics, Power series, Principal branch, Principal value, Pythagorean theorem, Python (programming language), Radian, Range of a function, Right triangle, Sign function, Sine and cosine, Springer Science+Business Media, Square root, Subset, SymPy, Tangent half-angle formula, Taylor series, Trigonometric functions, Trigonometric functions of matrices, Unit circle, University of Konstanz, Versine, Well-defined expression, Wolfram Mathematica.

Inverse trigonometric functions, the Glossary

Table of Contents

See also

Elementary special functions

Mathematical relations

References