> ## 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If you encounter incorrect, outdated, or confusing documentation on this page, submit feedback: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/acos",
  "feedback": "Description of the issue"
}
```

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

</AgentInstructions>

# acos

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

Use the `acos` function in APL to compute the arc cosine (inverse cosine) of a numeric expression. The function returns the angle, in radians, whose cosine equals the input value. The input must be in the range \[-1, 1]; values outside this range return `null`.

`acos` is useful when you work with normalized ratios or rates that fall in the \[-1, 1] range and you need to encode them as angular values. For example, you can use `acos` to convert a normalized success rate into a phase angle for cyclic analysis or signal processing.

## 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">
    In Splunk SPL, `acos()` is available in the `eval` command and works identically: it returns the arc cosine in radians for inputs in \[-1, 1].

    <CodeGroup>
      ```sql Splunk example theme={null}
      | eval angle = acos(normalized_rate)
      ```

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

  <Accordion title="ANSI SQL users">
    In ANSI SQL, `ACOS()` is a standard mathematical function with the same semantics. Pass a value in \[-1, 1] to receive the arc cosine in radians.

    <CodeGroup>
      ```sql SQL example theme={null}
      SELECT ACOS(normalized_rate) AS angle FROM logs
      ```

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

## Usage

### Syntax

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

### Parameters

| Name | Type | Required | Description                          |
| ---- | ---- | -------- | ------------------------------------ |
| `x`  | real | Yes      | A real number in the range \[-1, 1]. |

### Returns

* The arc cosine of `x` in radians, in the range \[0, π].
* `null` if `x` \< -1 or `x` > 1.

## Example

Use `acos` to compute the arccosine of a value and return the angle in radians.

**Query**

```kusto theme={null}
print result = acos(0.5)
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%20%22print%20result%20%3D%20acos%280.5%29%22%7D)

**Output**

| result |
| ------ |
| 1.0472 |

## List of related functions

* [asin](/apl/scalar-functions/mathematical-functions/asin): Returns the arc sine. Use it when the input value maps to a sine rather than a cosine.
* [atan](/apl/scalar-functions/mathematical-functions/atan): Returns the arc tangent. Use it when the input is not constrained to \[-1, 1].
* [cos](/apl/scalar-functions/mathematical-functions/cos): Returns the cosine. Use it to apply the forward transformation before using `acos` as the inverse.
* [radians](/apl/scalar-functions/mathematical-functions/radians): Converts degrees to radians. Use it to convert angle output from `acos` into degrees.
* [degrees](/apl/scalar-functions/mathematical-functions/degrees): Converts radians to degrees. Use it if you need the `acos` result expressed in degrees.