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Inverse trigonometric functions

Index 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). [1]

68 relations: A K Peters, Analytic function, Argument (complex analysis), Atan2, Binomial series, Bookboon, Branch point, C (programming language), Cambridge University Press, Carl Friedrich Gauss, Complex logarithm, Complex number, Complex plane, Condition number, Degree (angle), Derivative, Domain coloring, Domain of a function, Dover Publications, Empty product, Encyclopedia Americana, Engineering, Exsecant, Generalized continued fraction, Geometric series, Geometry, Henry Holt and Company, Hypergeometric function, Improper integral, Injective function, 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, List of trigonometric identities, Macmillan Publishers, Mathematics, Multiplicative inverse, Multivalued function, Navigation, Nuclear Instruments and Methods in Physics Research, Physics, ..., Power series, Principal branch, Principal value, Pythagorean theorem, Radian, Range (mathematics), Right triangle, ScienceDirect, Sine, Springer Science+Business Media, Square root, Subset, Tangent half-angle formula, Taylor series, Trigonometric functions, Unit circle, University of Konstanz, Versine. Expand index (18 more) »

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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Analytic function

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

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Argument (complex analysis)

In mathematics, the argument is a multi-valued function operating on the nonzero complex numbers.

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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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Binomial series

In mathematics, the binomial series is the Maclaurin series for the function f given by f(x).

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Bookboon

Bookboon is currently the world's largest online publishing company of eBooks.

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Branch point

In the mathematical field of complex analysis, a branch point of a multi-valued function (usually referred to as a "multifunction" in the context of complex analysis) is a point such that the function is discontinuous when going around an arbitrarily small circuit around this point.

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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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Cambridge University Press

Cambridge University Press (CUP) is the publishing business 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 and physicist who made significant contributions to many fields, including algebra, analysis, astronomy, differential geometry, electrostatics, geodesy, geophysics, magnetic fields, matrix theory, mechanics, number theory, optics and statistics.

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Complex logarithm

In complex analysis, a complex logarithm of the non-zero complex number, denoted by, is defined to be any complex number for which.

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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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Complex plane

In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the perpendicular imaginary axis.

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Condition number

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

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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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Domain coloring

In mathematics, domain coloring or a color wheel graph is a technique for visualizing complex functions, which assigns a color to each point of the complex plane.

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Domain of a function

In mathematics, and more specifically in naive set theory, the domain of definition (or simply the domain) of a function is the set of "input" or argument values for which the function is defined.

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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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Empty product

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

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Encyclopedia Americana

Encyclopedia Americana is one of the largest general encyclopedias in the English language.

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Engineering

Engineering is the creative application of science, mathematical methods, and empirical evidence to the innovation, design, construction, operation and maintenance of structures, machines, materials, devices, systems, processes, and organizations.

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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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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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Geometric series

In mathematics, a geometric series is a series with a constant ratio between successive terms.

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Geometry

Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

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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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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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Improper integral

In mathematical analysis, an improper integral is the limit of a definite integral as an endpoint of the interval(s) of integration approaches either a specified real number, \infty, -\infty, or in some instances as both endpoints approach limits.

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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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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 their derivative and antiderivative.

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Integration by substitution

In calculus, integration by substitution, also known as u-substitution, is a method for finding integrals.

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International Organization for Standardization

The International Organization for Standardization (ISO) is an international standard-setting body composed of representatives from various national standards organizations.

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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 hyperbolic functions

In mathematics, the inverse hyperbolic functions are the inverse functions of the hyperbolic 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).

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John Herschel

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

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Lahore

Lahore (لاہور, لہور) is the capital city of the Pakistani province of Punjab, and is the country’s second-most populous city after Karachi.

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Leibniz formula for π

In mathematics, the Leibniz formula for pi, named after Gottfried Leibniz, states that It is also called Madhava–Leibniz series as it is a special case of a more general series expansion for the inverse tangent function, first discovered by the Indian mathematician Madhava of Sangamagrama in the 14th century, the specific case first published by Leibniz around 1676.

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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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Letter case

Letter case (or just case) is the distinction between the letters that are in larger upper case (also uppercase, capital letters, capitals, caps, large letters, or more formally majuscule) and smaller lower case (also lowercase, small letters, 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 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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Macmillan Publishers

Macmillan Publishers Ltd (occasionally known as the Macmillan Group) is an international publishing company owned by Holtzbrinck Publishing Group.

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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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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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Multivalued function

In mathematics, a multivalued function from a domain to a codomain is a heterogeneous relation.

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Navigation

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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Physics

Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.

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Power series

In mathematics, a power series (in one variable) is an infinite series of the form where an represents the coefficient of the nth term and c is a constant.

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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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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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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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Range (mathematics)

In mathematics, and more specifically in naive set theory, the range of a function refers to either the codomain or the image of the function, depending upon usage.

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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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ScienceDirect

ScienceDirect is a website which provides subscription-based access to a large database of scientific and medical research.

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Sine

In mathematics, the sine is a trigonometric function of an angle.

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Springer Science+Business Media

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes 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 a is a number y such that; in other words, a number y whose square (the result of multiplying the number by itself, or) is a. For example, 4 and −4 are square roots of 16 because.

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Subset

In mathematics, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.

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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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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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Unit circle

In mathematics, a unit circle is a circle with a radius of one.

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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 already appearing in some of the earliest trigonometric tables.

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Redirects here:

Acos, 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 cosecant, Arc cosine, Arc cotangent, Arc function, Arc functions, Arc sine, Arc tangent, Arc trigonometric function, Arc trigonometric functions, 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, Arccot, Arccot (trigonometry), Arccotangent, Arccsc, Arccsc (trigonometry), Arcctg, Arcctg (trigonometric function), Arcsec (function), Arcsec (trigonometric function), Arcsec (trigonometry), Arcsecant, Arcsin, Arcsin (trigonometry), Arcsin(x), Arcsine, Arctan, Arctan (trigonometry), Arctan(x), Arctangent, Arctg, Arctg (trigonometric function), Arcus cosecans, Arcus cosinus, Arcus cotangens, Arcus function, Arcus secans, Arcus sinus, Arcus tangens, Asec (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 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.

References

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

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