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

<AgentInstructions>

## Submitting Feedback

If you encounter incorrect, outdated, or confusing documentation on this page, submit feedback:

POST https://axiom.co/docs/feedback

```json
{
  "path": "/apl/scalar-functions/mathematical-functions/cot",
  "feedback": "Description of the issue"
}
```

Only submit feedback when you have something specific and actionable to report.

</AgentInstructions>

# cot

> This page explains how to use the cot function in APL.

Use the `cot` function in APL to compute the cotangent of an angle expressed in radians. The cotangent is the reciprocal of the tangent: `cot(x) = cos(x) / sin(x)`. The function is undefined at multiples of π, where the sine is zero.

`cot` is useful when you work with angular or cyclic calculations and need the cotangent as part of a larger formula. In observability, you might use it to transform normalized metric ratios into angular coordinates for signal analysis.

## For users of other query languages

If you come from other query languages, this section explains how to adjust your existing queries to achieve the same results in APL.

<AccordionGroup>
  <Accordion title="Splunk SPL users">
    Splunk SPL doesn't include a built-in `cot()` function. You compute it as the reciprocal of `tan()`.

    <CodeGroup>
      ```sql Splunk example theme={null}
      | eval cot_val = 1 / tan(angle_rad)
      ```

      ```kusto APL equivalent theme={null}
      ['sample-http-logs']
      | extend cot_val = cot(angle_rad)
      ```
    </CodeGroup>
  </Accordion>

  <Accordion title="ANSI SQL users">
    ANSI SQL does not define a standard `COT()` function, though SQL Server provides one. In PostgreSQL and other databases, you compute it as `1 / TAN(x)`.

    <CodeGroup>
      ```sql SQL example theme={null}
      SELECT 1.0 / TAN(angle_rad) AS cot_val FROM logs
      ```

      ```kusto APL equivalent theme={null}
      ['sample-http-logs']
      | extend cot_val = cot(angle_rad)
      ```
    </CodeGroup>
  </Accordion>
</AccordionGroup>

## Usage

### Syntax

```kusto theme={null}
cot(x)
```

### Parameters

| Name | Type | Required | Description                                        |
| ---- | ---- | -------- | -------------------------------------------------- |
| `x`  | real | Yes      | The angle in radians. Must not be a multiple of π. |

### Returns

The cotangent of `x`. Returns infinity or `null` when `sin(x)` equals zero (that is, when `x` is a multiple of π).

## Example

Use `cot` to compute the cotangent of an angle in radians.

**Query**

```kusto theme={null}
print result = cot(pi() / 4)
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%20%22print%20result%20%3D%20cot%28pi%28%29%20/%204%29%22%7D)

**Output**

| result |
| ------ |
| 1.0000 |

## List of related functions

* [tan](/apl/scalar-functions/mathematical-functions/tan): Returns the tangent, the reciprocal of `cot`. Use it as the primary trigonometric ratio when cotangent is not needed.
* [sin](/apl/scalar-functions/mathematical-functions/sin): Returns the sine. Use it along with `cos` to compute cotangent manually as `cos(x)/sin(x)`.
* [cos](/apl/scalar-functions/mathematical-functions/cos): Returns the cosine. Use it in combination with `sin` for manual cotangent calculation.
* [atan](/apl/scalar-functions/mathematical-functions/atan): Returns the arc tangent. Use it as the inverse of `tan` when you need to recover an angle.
* [radians](/apl/scalar-functions/mathematical-functions/radians): Converts degrees to radians. Use it to prepare degree-based angle inputs before calling `cot`.