acoth

Inverse hyperbolic cotangent

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Syntax

Y = acoth(X)

Description

example

Y = acoth(X) returns the inverse hyperbolic cotangent 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 cotangent of the elements of vector X. The acoth function acts on X element-wise.

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

   0.5493 + 0.0000i  -0.3466 + 0.0000i   0.1733 - 0.3927i
Open Live Script

Plot the inverse hyperbolic cotangent function over the intervals -30≤x<-1 and 1<x≤30.

x1 = -30:0.1:-1.1; 
x2 = 1.1:0.1:30; 
plot(x1,acoth(x1),x2,acoth(x2))
grid on
xlabel('x')
ylabel('acoth(x)')

Input Arguments

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

Data Types: single | double
Complex Number Support: Yes

More About

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Inverse Hyperbolic Cotangent

For real values x in the domain − ∞<x<−1 and 1<x<∞, the inverse hyperbolic cotangent satisfies

coth−1(x)=tanh−1(1x)=12log(x+1x−1).

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

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

See Also

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Introduced before R2006a

MATLAB Documentation

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