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Domain of cotangent and cosecant : The domains of and are the same. They are the set of all angles θ {\displaystyle \theta } at which sin θ ≠ 0 , {\displaystyle \sin \theta \neq 0,} i.e. all real numbers that are not of the form π n {\displaystyle \pi n} for some integer n , {\displaystyle n,}
Domain of cotangent and cosecant : The domains of and are the same. They are the set of all angles θ {\displaystyle \theta } at which sin θ ≠ 0 , {\displaystyle \sin \theta \neq 0,} i.e. all real numbers that are not of the form π n {\displaystyle \pi n} for some integer n , {\displaystyle n,}
For all inverse hyperbolic functions, the principal value may be defined in terms of principal values of the square root and the logarithm function. However, in some cases, the formulas of § Definitions in terms of logarithms do not give a correct principal value, as giving a domain of definition which is too small and, in one case non-connected.
To define a true inverse function, one must restrict the domain to an interval where the function is monotonic, and is thus bijective from this interval to its image by the function. The common choice for this interval, called the set of principal values, is given in the following table. As usual, the inverse trigonometric functions are denoted ...
By restricting the domain of a trigonometric function, however, they can be made invertible. [42]: 48ff The names of the inverse trigonometric functions, together with their domains and range, can be found in the following table: [42]: 48ff [43]: 521ff
arcosh – inverse hyperbolic cosine function. arcoth – inverse hyperbolic cotangent function. arcsch – inverse hyperbolic cosecant function. (Also written as arcosech.) arcsec – inverse secant function. arcsin – inverse sine function. arctan – inverse tangent function. arctan2 – inverse tangent function with two arguments. (Also ...
Trigonometric functions and their reciprocals on the unit circle. All of the right-angled triangles are similar, i.e. the ratios between their corresponding sides are the same.
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