# sech

Hyperbolic secant

## Description

example

Y = sech(X) returns the hyperbolic secant of the elements of X. The sech function operates element-wise on arrays. The function accepts both real and complex inputs. All angles are in radians.

## Examples

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Create a vector and calculate the hyperbolic secant of each value.

X = [0 pi 2*pi 3*pi];
Y = sech(X)
Y = 1×4

1.0000    0.0863    0.0037    0.0002

Plot the hyperbolic secant over the domain $-2\pi \le x\le 2\pi$.

x = -2*pi:0.01:2*pi;
y = sech(x);
plot(x,y)
grid on

## Input Arguments

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Input angles in radians, specified as a scalar, vector, matrix, multidimensional array, table, or timetable.

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

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### Hyperbolic Secant

The hyperbolic secant of x is equal to the inverse of the hyperbolic cosine

$\text{sech}\left(x\right)=\frac{1}{\mathrm{cosh}\left(x\right)}=\frac{2}{{e}^{x}+{e}^{-x}}.$

In terms of the traditional secant function with a complex argument, the identity is

$\text{sech}\left(x\right)=\mathrm{sec}\left(ix\right)\text{\hspace{0.17em}}.$

## Version History

Introduced before R2006a

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