> ## Documentation Index
> Fetch the complete documentation index at: https://docs.firebolt.io/llms.txt
> Use this file to discover all available pages before exploring further.

> Reference material for COTH function

# COTH

Calculates the hyperbolic cotangent of a provided value.

## Syntax

```sql theme={"theme":{"light":"css-variables","dark":"css-variables"}}
COTH(<value>)
```

## Parameters

| Parameter | Description                                                  | Supported input types |
| :-------- | :----------------------------------------------------------- | :-------------------- |
| `<value>` | The value that determines the returned hyperbolic cotangent. | `DOUBLE PRECISION`    |

## Return Type

`DOUBLE PRECISION`

`COTH` is the reciprocal of `TANH`, which is zero only at zero, so an argument of zero raises a division-by-zero error. A large argument gives an infinite hyperbolic tangent, whose reciprocal is zero.

## Example

`COTH` is `1 / TANH`, so at `LN(2)` it is `1 / 0.6`, or `5/3`:

<div className="query-window">
  ```
  SELECT COTH(LN(2)) as result;
  ```

  | result <span>double</span> |
  | :------------------------- |
  | 1.6666666666666667         |

  <p><span>Rows: 1</span><span>Execution time: 5.21ms</span></p>
</div>

`COTH` approaches 1 as its argument grows:

<div className="query-window">
  ```
  SELECT COTH(2) as result;
  ```

  | result <span>double</span> |
  | :------------------------- |
  | 1.0373147207275482         |

  <p><span>Rows: 1</span><span>Execution time: 5.21ms</span></p>
</div>