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See the recommended documentation of this function

# acosh

hyperbolic cosine inverse

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
])

• cosh — гиперболический косинус
• sinh — гиперболический синус
• tanh — гиперболический тангенс