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# acosh

hyperbolic cosine inverse

### Syntax

`t = acosh(x)`

### Arguments

x, t

each is a real or complex vector or matrix. `t` has the sizes of `x`.

### Description

`acosh(x)` returns `t` such that `cosh(t)==x` and `real(t)>=0`. `-t` are always other possible answers.

For real input numbers `-1 < x < 1`, `real(t)==0` and `imag(t)` belongs to `]0, %pi[`.

For complex numbers `x`, `imag(t)` belongs to `[-pi, pi]` and any `t + k*%pi*%i` with integer k are other possible answers.

### Examples

```x = [ -2 -1.001 -1 -0.999 -0.5  0
2  1.001  1  0.999  0.5  0]'
t = acosh(x)
cosh(t) - x
cosh(-t) - x

// With complex numbers:
acosh([-0.01*%i  0.01*%i
-0.1*%i   0.1*%i
-%i       %i
-10*%i    10*%i
-1 - %i,  1 + %i
-2 - 2*%i, 2 + 2*%i
])```

### See also

• cosh — co-seno hiperbólico
• sinh — seno hiperbólico
• tanh — tangente hiperbólica
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