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In mathematics, the inverse trigonometric functions (occasionally also called arcus functions, [1][2][3][4][5] antitrigonometric functions[6] or cyclometric functions[7][8][9]) are the inverse functions of the trigonometric functions, under suitably restricted domains. Specifically, they are the inverses of the sine, cosine, tangent, cotangent ...
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] [2] are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
The trigonometric functions of angles that are multiples of 15°, 18°, or 22.5° have simple algebraic values. These values are listed in the following table for angles from 0° to 45°. [1] In the table below, the label "Undefined" represents a ratio If the codomain of the trigonometric functions is taken to be the real numbers these entries ...
Small-angle approximation. Approximately equal behavior of some (trigonometric) functions for x → 0. The small-angle approximations can be used to approximate the values of the main trigonometric functions, provided that the angle in question is small and is measured in radians: These approximations have a wide range of uses in branches of ...
Functor. List of specific functions. v. t. e. In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by. For a function , its inverse admits an explicit description: it sends each element ...
In mathematics, tables of trigonometric functions are useful in a number of areas. Before the existence of pocket calculators, trigonometric tables were essential for navigation, science and engineering. The calculation of mathematical tables was an important area of study, which led to the development of the first mechanical computing devices.
The angle between the horizontal line and the shown diagonal is 1 2 (a + b). This is a geometric way to prove the particular tangent half-angle formula that says tan 1 2 (a + b) = (sin a + sin b) / (cos a + cos b). The formulae sin 1 2 (a + b) and cos 1 2 (a + b) are the ratios of the actual distances to the length ...
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. The latter, half a versine, is of particular importance in the haversine ...