arccosh
The inverse hyperbolic cosine function.
Syntax
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arccosh(x)-
xis a real or complex number
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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