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Trigonometric functions of inverse trigonometric functions are tabulated below. A quick way to derive them is by considering the geometry of a right-angled triangle, with one side of length 1 and another side of length , then applying the Pythagorean theorem and definitions of the trigonometric ratios.
The versine or versed sine is a trigonometric function found in some of the earliest (Sanskrit Aryabhatia, [1] Section I) trigonometric tables. The versine of an angle is 1 minus its cosine . There are several related functions, most notably the coversine and haversine .
5.1 Physics. 5.2 Astronomy. 5.3 Chemistry. ... List of integrals of inverse trigonometric functions; ... Dave's short trig course;
There are three common notations for inverse trigonometric functions. The arcsine function, for instance, could be written as sin −1, asin, or, as is used on this page, arcsin. For each inverse trigonometric integration formula below there is a corresponding formula in the list of integrals of inverse hyperbolic functions.
The names exsecant, versine, chord, etc. can also be applied to line segments related to a circular arc. [2] The length of each segment is the radius times the corresponding trigonometric function of the angle. The external secant function (abbreviated exsecant, symbolized exsec) is a trigonometric function defined in terms of the secant function:
An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition, [8] as explained here. This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms.
Basis of trigonometry: if two right triangles have equal acute angles, they are similar, so their corresponding side lengths are proportional.. In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) [1] are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
There are six in common use: inverse hyperbolic sine, inverse hyperbolic cosine, inverse hyperbolic tangent, inverse hyperbolic cosecant, inverse hyperbolic secant, and inverse hyperbolic cotangent. They are commonly denoted by the symbols for the hyperbolic functions, prefixed with arc- or ar- , or with a superscript − 1 {\displaystyle {-1 ...