arccosh
The inverse hyperbolic cosine function.
Syntax

arccosh(x)

x
is a real or complex number

Description
arccosh
is the inverse of the restriction of the hyperbolic cosine function to [0, ∞). For real numbers, the domain is [1, ∞). It is defined by
arccosh(z) = ln(z + √(z + 1)⋅√(z − 1))
for all complex z
. This formula is also used for real numbers less than 1.
Notes
This function is also called arcosh
(area hyperbolic cosine) in the literature. Some authors claim that the name arccosh
is a misnomer, but this depends crucially on how you view the connections between the trigonometric and the hyperbolic functions and their (restriction) inverses. One can argue that the name arccosh
makes perfect sense.
Examples
arccosh(1)
0
arccosh(π)
1.81152627246
arccosh(0)
1.57079632679⋅i
arccosh(i)
0.88137358702 + 1.57079632679⋅i