acosh

Inverse hyperbolic cosine

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Syntax

Y = acosh(X)

Description

example

Y = acosh(X) returns the inverse hyperbolic cosine of the elements of X. The function accepts both real and complex inputs. All angles are in radians.

Examples

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Open Live Script

Find the inverse hyperbolic cosine of the elements of vector X. The acosh function acts on X element-wise.

X = [2 -3 1+2i];
Y = acosh(X)
Y = 1×3 complex

   1.3170 + 0.0000i   1.7627 + 3.1416i   1.5286 + 1.1437i
Open Live Script

Plot the inverse hyperbolic cosine function over the interval 1≤x≤5.

x = 1:0.01:5; 
plot(x,acosh(x))
grid on
xlabel('x')
ylabel('acosh(x)')

Input Arguments

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Hyperbolic cosine of angle, specified as a scalar, vector, matrix, or multidimensional array. The acosh operation is element-wise when X is nonscalar.

Data Types: single | double
Complex Number Support: Yes

More About

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Inverse Hyperbolic Cosine

For real values x in the domain x>1, the inverse hyperbolic cosine satisfies

cosh−1(x)=log(x+x2−1).

For complex numbers z=x+iy, as well as real values in the domain − ∞<z≤  1, the call acosh(z) returns complex results.

Extended Capabilities

See Also

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Introduced before R2006a

MATLAB Documentation

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