acsch

Inverse hyperbolic cosecant

Syntax

Y = acsch(X)

Description

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

Examples

Inverse Hyperbolic Cosecant of Vector

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

X = [2 -3 1+2i];
Y = acsch(X)

Y = 1×3 complex

   0.4812 + 0.0000i  -0.3275 + 0.0000i   0.2156 - 0.4016i

Plot the Inverse Hyperbolic Cosecant Function

Plot the inverse hyperbolic cosecant function over the intervals $$-20\le x\le -1$$ and $$1\le x\le 20$$.

x1 = -20:0.01:-1; 
x2 = 1:0.01:20; 
plot(x1,acsch(x1),x2,acsch(x2))
grid on
xlabel('x')
ylabel('acsch(x)')

Input Arguments

X — Hyperbolic cosecant of angle

scalar | vector | matrix | multidimensional array

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

Data Types: single | double
Complex Number Support: Yes

More About

Inverse Hyperbolic Cosecant

For real values $$x$$ in the domain $$x<0$$ and $$x>0$$, the inverse hyperbolic cosecant satisfies

$${\text{csch}}^{-1}\left(z\right)={\sinh }^{-1}\left(\frac{1}{z}\right)=\log \left(\frac{1}{x}+\sqrt{\frac{1}{x^2}+1}\right).$$

For complex numbers $$z=x+iy$$, the call acsch(z) returns complex results.

Extended Capabilities

Tall Arrays

Calculate with arrays that have more rows than fit in memory.

This function fully supports tall arrays. For more information, see Tall Arrays.

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

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Distributed Arrays

Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).