The SECH function returns the hyperbolic secant of an angle.

  • This function was introduced in Excel 2013 and so is not available in earlier versions.

Syntax

=SECH(number)

Arguments

Argument Description
number The number argument is the angle, in radians, for which you want the hyperbolic secant

  The absolute value of number must be less than 2^27

Examples

  A B C
1 Formula Result Notes
2 =SECH(0.785398) 0.75494 The hyperbolic secant of a 45 degree angle
3 =SECH(RADIANS(45)) 0.75494 The hyperbolic secant of a 45 degree angle
4 =SECH(PI()/4) 0.75494 The hyperbolic secant of a 45 degree angle

Note: If the angle is in degrees, you need to be convert it to radians before supplying it to the SECH function. You can convert it, using the RADIANS function: =RADIANS(degrees)

Common Function Error(s)

Problem What went wrong
#VALUE! Occurs if the supplied number argument is not a numeric value
#NUM! Occurs if the supplied number argument is less than -2^27 or is greater than 2^27

The hyperbolic secant is the reciprocal of the hyperbolic cosine. The value for hyperbolic secant is given by the following equation:  

    \[    sech(x) = \frac 1{cosh(x)} = \frac 2{(e^x = e^{-x})}    \]

See Wikipedia for more information on hyperbolic functions.