Takes the hyperbolic secant of a number.

sech(*value*)

**Menu Location**

- Press 2nd MATH to enter the MATH menu.
- Press C to enter the Hyperbolic submenu.
- Press 5 to select sech(.

This command requires a calculator with AMS version 2.07 or higher (it will also work on any TI-89 Titanium or Voyage 200 calculator)

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The `sech()` command returns the hyperbolic secant of a number. Along with 11 other trig and hyperbolic functions, it was added in AMS version 2.07; on earlier versions, `sech(x)` can be replaced by 1/`cosh(x)`.

As long as the calculator is in radian mode, `sech()` can be used with complex numbers according to the rule that `sech(ix)`=

`sec(x)`and

`sec(`=

**x)***i*`sech(x)`. This rule only works in radian mode, and

`sech()`of a complex number will return a domain error when working in degrees or gradians.

Occasionally, `sech()` can compute an exact result; most of the time, the calculator will leave an expression with `sech()` alone unless it's in approximate mode (or you force an approximation). When `sech()` is used with symbolic expressions, the calculator can go back and forth between the `sech()` expression and its exponential equivalent.

```
:sech(0)
1
:expand(sech(x))
2*e^x/((e^x)^2+1)
:comDenom(2*e^x/((e^x)^2+1))
1/cosh(x)
```

If `sech()` is applied to a list, it will take the hyperbolic secant of every element in the list. However, it can't be applied to matrices the way `cosh()` can (this is probably an oversight; all the trig and hyperbolic functions that were present in all AMS versions work with matrices, but the ones added in version 2.07 do not).

# Formulas

The definition of hyperbolic secant is, by analogy with `sec()`, the reciprocal of `cosh()`:

# Error Conditions

**260 - Domain error** happens when taking sech() of a complex number in degree or gradian mode.