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.

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Areasinus hyperbolicus (abgekürzt oder ) und Areakosinus hyperbolicus (abgekürzt oder ) gehören zu den Areafunktionen und sind die Umkehrfunktionen von Sinus hyperbolicus und Kosinus hyperbolicus. Die Funktionen lassen sich durch die folgenden Formeln ausdrücken: Areasinus hyperbolicus: Definition über den natürlichen Logarithmus :

Feb 3, 2020 · arcosh can be calculated directly, using a logarithm function, like this: arcosh x = ln (x + x 2 − 1) Here is a proof of the logarithm formula for arcosh. It is very similar to the proof for arsinh. We will use: u = arcosh x. The cosh of u will be x, because cosh is the inverse of arcosh: x = cosh u. One form of the formula for cosh is:

Inverse hyperbolic cosine is often written as arccosh, but usually abbreviated as "acosh" or "arcosh", as in the following equation: arccosh (y) = acosh (y) = arcosh (y) arccosh(y) = acosh(y) = arcosh(y) Where it is the inverse of hyperbolic cosine, or: x=arccosh (y)\\y=cosh (x) x = arccosh(y) y = cosh(x)

Jan 3, 2025 · The “c” in arcsin x, arccos x, arctan x indicates the circular functions. The hyperbolic functions have “h”, but the “h” doesn’t come immediately after the “ar”: arsinh x, arcosh x, artanh x. Be careful not to confuse these, especially when looking them up in the formulae booklet

What is the integral of arccosh (x) ?

It's not true that arcosh(coshx) = x, because this holds only for x ≥ 0. The function x ↦ coshx is invertible in the interval [0, ∞) (where it assumes all the values in [1, ∞)), because it is increasing. Therefore one can define a function arcosh: [1, ∞) → [0, ∞) such that arcosh(coshx) = x and cosh(arcoshy) = y, for all x ≥ 0 and all y ≥ 1.

Jun 20, 2020 · This tool evaluates the inverse hyperbolic cosine of a number: arcosh(x). Enter the argument x below.

May 3, 2023 · arcosh(x) = i arcsin(x) + C = i arccos(x) + C. Since arcsin(x) = π2 − arccos(x). Is this believable (with C = 0)? Well, yes. It is true that cosh(iy) = cos(y) and applying cosh to both sides finds: x = cosh(arcosh(x)) =? cosh(i arccos(x)) = cos(arccos(x)) = x.