Main Content

acoth

Inverse hyperbolic cotangent

collapse all in page

Syntax

Y = acoth(X)

Description

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.

example

Examples

collapse all

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)')

Figure contains an axes object. The axes object with xlabel x, ylabel acoth(x) contains 2 objects of type line.

Input Arguments

collapse all

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

Data Types: single | double | table | timetable
Complex Number Support: Yes

More About

collapse all

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™.

Version History

Introduced before R2006a

expand all

See Also

| | | |