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Co (function Prefix)
In mathematics, a function ''f'' is cofunction of a function ''g'' if ''f''(''A'') = ''g''(''B'') whenever ''A'' and ''B'' are complementary angles. This definition typically applies to trigonometric functions. The prefix "co-" can be found already in Edmund Gunter's ''Canon triangulorum'' (1620). For example, sine (Latin: ''sinus'') and cosine (Latin: ''cosinus'', ''sinus complementi'') are cofunctions of each other (hence the "co" in "cosine"): The same is true of secant (Latin: ''secans'') and cosecant (Latin: ''cosecans'', ''secans complementi'') as well as of tangent (Latin: ''tangens'') and cotangent (Latin: ''cotangens'', ''tangens complementi''): These equations are also known as the cofunction identities. This also holds true for the versine (versed sine, ver) and coversine (coversed sine, cvs), the vercosine (versed cosine, vcs) and covercosine (coversed cosine, cvc), the haversine (half-versed sine, hav) and hacoversine (half-coversed sine, hcv), the havercosin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sine Cosine One Period
In mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that of the hypotenuse. For an angle \theta, the sine and cosine functions are denoted simply as \sin \theta and \cos \theta. More generally, the definitions of sine and cosine can be extended to any real value in terms of the lengths of certain line segments in a unit circle. More modern definitions express the sine and cosine as infinite series, or as the solutions of certain differential equations, allowing their extension to arbitrary positive and negative values and even to complex numbers. The sine and cosine functions are commonly used to model periodic phenomena such as sound and lig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hacoversine
The versine or versed sine is a trigonometric function found in some of the earliest (Sanskrit ''Aryabhatia'', Section I) s. The versine of an angle is 1 minus its cosine. There are several related functions, most notably the coversine and haversine. The latter, half a versine, is of particular importance in the of navigation. Overview The versine[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MathWorld
''MathWorld'' is an online mathematics reference work, created and largely written by Eric W. Weisstein. It is sponsored by and licensed to Wolfram Research, Inc. and was partially funded by the National Science Foundation's National Science Digital Library grant to the University of Illinois at Urbana–Champaign. History Eric W. Weisstein, the creator of the site, was a physics and astronomy student who got into the habit of writing notes on his mathematical readings. In 1995 he put his notes online and called it "Eric's Treasure Trove of Mathematics." It contained hundreds of pages/articles, covering a wide range of mathematical topics. The site became popular as an extensive single resource on mathematics on the web. Weisstein continuously improved the notes and accepted corrections and comments from online readers. In 1998, he made a contract with CRC Press and the contents of the site were published in print and CD-ROM form, titled "CRC Concise Encyclopedia of Mathematic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Henry Holt And Company
Henry Holt and Company is an American book-publishing company based in New York City. One of the oldest publishers in the United States, it was founded in 1866 by Henry Holt and Frederick Leypoldt. Currently, the company publishes in the fields of American and international fiction, biography, history and politics, science, psychology, and health, as well as books for children's literature. In the US, it operates under Macmillan Publishers. History The company publishes under several imprints, including Metropolitan Books, Times Books, Owl Books, and Picador. It also publishes under the name of Holt Paperbacks. The company has published works by renowned authors Erich Fromm, Paul Auster, Hilary Mantel, Robert Frost, Hermann Hesse, Norman Mailer, Herta Müller, Thomas Pynchon, Robert Louis Stevenson, Ivan Turgenev, and Noam Chomsky. From 1951 to 1985, Holt published the magazine ''Field & Stream''. Holt merged with Rinehart & Company of New York and the John C. Winston Compa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cengage Learning
Cengage Group is an American educational content, technology, and services company for the higher education, K-12, professional, and library markets. It operates in more than 20 countries around the world.(Jun 27, 2014Global Publishing Leaders 2014: Cengage publishersweekly.comCompany Info - Wall Street JournalCengage LearningCompany Overview of Cengage Learning, Inc. BloombergBusiness Company information The company is headquartered in Boston, Massachusetts, and has approximately 5,000 employees worldwide across nearly 38 countries. It was headquartered at its Stamford, Connecticut, office until April 2014. |
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. Geometrically, these are identities involving certain functions of one or more angles. They are distinct from triangle identities, which are identities potentially involving angles but also involving side lengths or other lengths of a triangle. These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common technique involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity. Pythagorean identities The basic relationship between the sine and cosine is given by the Pythagorean identity: :\sin^2\theta + \cos^2\theta = 1, where \sin^2 \theta means (\sin \theta)^2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Covariance
In probability theory and statistics, covariance is a measure of the joint variability of two random variables. If the greater values of one variable mainly correspond with the greater values of the other variable, and the same holds for the lesser values (that is, the variables tend to show similar behavior), the covariance is positive. In the opposite case, when the greater values of one variable mainly correspond to the lesser values of the other, (that is, the variables tend to show opposite behavior), the covariance is negative. The sign of the covariance therefore shows the tendency in the linear relationship between the variables. The magnitude of the covariance is not easy to interpret because it is not normalized and hence depends on the magnitudes of the variables. The normalized version of the covariance, the correlation coefficient, however, shows by its magnitude the strength of the linear relation. A distinction must be made between (1) the covariance of two random ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cologarithm
In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number to the base is the exponent to which must be raised, to produce . For example, since , the ''logarithm base'' 10 of is , or . The logarithm of to ''base'' is denoted as , or without parentheses, , or even without the explicit base, , when no confusion is possible, or when the base does not matter such as in big O notation. The logarithm base is called the decimal or common logarithm and is commonly used in science and engineering. The natural logarithm has the number as its base; its use is widespread in mathematics and physics, because of its very simple derivative. The binary logarithm uses base and is frequently used in computer science. Logarithms were introduced by John Napier in 1614 as a means of simplifying calculations. They were rapidly adopted by navigators, scientists, engineers, surveyors and others to perform high-accu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacobi Elliptic Cosine
In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum (see also pendulum (mathematics)), as well as in the design of electronic elliptic filters. While trigonometric functions are defined with reference to a circle, the Jacobi elliptic functions are a generalization which refer to other conic sections, the ellipse in particular. The relation to trigonometric functions is contained in the notation, for example, by the matching notation \operatorname for \sin. The Jacobi elliptic functions are used more often in practical problems than the Weierstrass elliptic functions as they do not require notions of complex analysis to be defined and/or understood. They were introduced by . Carl Friedrich Gauss had already studied special Jacobi elliptic functions in 1797, the lemniscate elliptic functions in particular, but his work was published much later. Overview There are twelve Jacobi elliptic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lemniscatic Cosine
In mathematics, the lemniscate elliptic functions are elliptic functions related to the arc length of the lemniscate of Bernoulli. They were first studied by Giulio Carlo de' Toschi di Fagnano, Giulio Fagnano in 1718 and later by Leonhard Euler and Carl Friedrich Gauss, among others. The lemniscate sine and lemniscate cosine functions, usually written with the symbols and (sometimes the symbols and or and are used instead) are analogous to the trigonometric functions sine and cosine. While the trigonometric sine relates the arc length to the chord length in a unit-diameter circle x^2+y^2 = x, the lemniscate sine relates the arc length to the chord length of a lemniscate \bigl(x^2+y^2\bigr)^2=x^2-y^2. The lemniscate functions have periods related to a number called the lemniscate constant, the ratio of a lemniscate's perimeter to its diameter. This number is a Quartic plane curve, quartic analog of the (Conic section, quadratic) , pi, ratio of perimeter to diameter of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperbolic Functions
In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points form a circle with a unit radius, the points form the right half of the unit hyperbola. Also, similarly to how the derivatives of and are and respectively, the derivatives of and are and respectively. Hyperbolic functions occur in the calculations of angles and distances in hyperbolic geometry. They also occur in the solutions of many linear differential equations (such as the equation defining a catenary), cubic equations, and Laplace's equation in Cartesian coordinates. Laplace's equations are important in many areas of physics, including electromagnetic theory, heat transfer, fluid dynamics, and special relativity. The basic hyperbolic functions are: * hyperbolic sine "" (), * hyperbolic cosine "" (),''Collins Concise Dictionary'', p. 328 from which are derived: * hyperbolic tangent "" (), * hyp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Excosecant
The exsecant (exsec, exs) and excosecant (excosec, excsc, exc) are trigonometric functions defined in terms of the secant and cosecant functions. They used to be important in fields such as surveying, railway engineering, civil engineering, astronomy, and spherical trigonometry and could help improve accuracy, but are rarely used today except to simplify some calculations. Exsecant The exsecant, (Latin: ''secans exterior'') also known as exterior, external, outward or outer secant and abbreviated as exsec or exs, is a trigonometric function defined in terms of the secant function sec(''θ''): \operatorname(\theta) = \sec(\theta) - 1 = \frac - 1. The name ''exsecant'' can be understood from a graphical construction of the various trigonometric functions from a unit circle, such as was used historically. sec(''θ'') is the secant line , and the exsecant is the portion of this secant that lies ''exterior'' to the circle (''ex'' is Latin for ''out of''). Excosecant A rela ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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