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Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions, [4] and are used to obtain an angle from any of the angle's trigonometric ratios. Inverse trigonometric functions are widely used in engineering, navigation, physics, and geometry.
Their reciprocals are respectively the cosecant, the secant, and the cotangent functions, which are less used. Each of these six trigonometric functions has a corresponding inverse function , and an analog among the hyperbolic functions .
In mathematics, the inverse hyperbolic functions are inverses of the hyperbolic functions, analogous to the inverse circular functions. 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.
hyperbolic cosecant " csch" or "cosech" (/ ˈ k oʊ s ɛ tʃ, ˈ k oʊ ʃ ɛ k / [3]) corresponding to the derived trigonometric functions. The inverse hyperbolic functions are: inverse hyperbolic sine " arsinh" (also denoted "sinh −1", "asinh" or sometimes "arcsinh ") [9] [10] [11] inverse hyperbolic cosine " arcosh" (also denoted "cosh −1 ...
Pages in category "Inverse trigonometric functions" ... Inverse cosecant; Inverse cosine; Inverse cotangent; Inverse covercosine; Inverse coversine; Inverse excosecant;
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,}
The angle opposite the leg of length 1 (this angle can be labeled φ = π/2 − θ) has cotangent equal to the length of the other leg, and cosecant equal to the length of the hypotenuse. In that way, this trigonometric identity involving the cotangent and the cosecant also follows from the Pythagorean theorem.
The cosine, cotangent, and cosecant are so named because they are respectively the sine, tangent, and secant of the complementary angle abbreviated to "co-". [ 32 ] With these functions, one can answer virtually all questions about arbitrary triangles by using the law of sines and the law of cosines . [ 33 ]