# sech() Function & Examples

Use the sech() trigonometry function in Calcul.io. Review its syntax, edit working examples, understand the result, and explore related math functions.

## sech

#### sech(x)

Try it yourself:

```calculio
sech(2)
1 / cosh(2)
```

[coth](https://calcul.io/function/coth/index.md)

[csch](https://calcul.io/function/csch/index.md)

[cosh](https://calcul.io/function/cosh/index.md)

---

## Calculate hyperbolic secant with sech

**sech(x)** is the reciprocal of hyperbolic cosine: `1 / cosh(x)`. For real x it is even, equals 1 at zero, and approaches zero as |x| grows.

## Relationships

Use [cosh](https://calcul.io/function/cosh/index.md) for its denominator and [tanh](https://calcul.io/function/tanh/index.md) for the identity `sech(x)^2 + tanh(x)^2 = 1`. It appears in localized pulse and probability-shaped models.

## Caveats

Unlike [sec](https://calcul.io/function/sec/index.md), sech is hyperbolic rather than circular. Complex inputs can encounter poles where cosh is zero. For exponential expressions, compare [exp](https://calcul.io/function/exp/index.md) and take care with extreme values.

[All functions](https://calcul.io/functions/index.md)