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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 the definition of the principal values of the inverse hyperbolic tangent and cotangent. In these formulas, the argument of the logarithm is real if and only if z is real. For artanh, this argument is in the real interval (−∞, 0] , if z belongs either to (−∞, −1] or to [1, ∞) .
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 ...
tan −1 y = tan −1 (x), sometimes interpreted as arctan(x) or arctangent of x, the compositional inverse of the trigonometric function tangent (see below for ambiguity) tan −1 x = tan −1 ( x ), sometimes interpreted as (tan( x )) −1 = 1 / tan( x ) = cot( x ) or cotangent of x , the multiplicative inverse (or reciprocal) of the ...
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
1.9 Miscellaneous – the triple cotangent identity. 1.10 Sum to product identities. ... 2.5 Proof of compositions of trig and inverse trig functions. 3 See also. 4 ...
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