> ## 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.
# series_sin
> This page explains how to use the series_sin function in APL.
The `series_sin` function in APL returns the sine of each element in a numeric array. It applies the mathematical sine function element by element, producing a new array of the same length.
You use `series_sin` when you want to transform numeric sequences into their trigonometric equivalents. This is useful for signal processing, data transformations, or preparing time series data for statistical and mathematical 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.
Splunk SPL doesn’t provide a direct equivalent to `series_sin` for arrays. Instead, you typically use the `eval` command with the `sin()` function to compute the sine of a single numeric value. In APL, `series_sin` applies `sin()` across an array in one step.
```sql Splunk example theme={null}
... | eval sin_val=sin(duration)
```
```kusto APL equivalent theme={null}
datatable(arr: dynamic)
[
dynamic([0, 1.57, 3.14])
]
| extend sin_values = series_sin(arr)
```
ANSI SQL provides the `SIN()` function, but it operates on single values rather than arrays. In APL, `series_sin` is vectorized and works directly on arrays without requiring iteration.
```sql SQL example theme={null}
SELECT SIN(duration) AS sin_val
FROM traces;
```
```kusto APL equivalent theme={null}
datatable(arr: dynamic)
[
dynamic([0, 1.57, 3.14])
]
| extend sin_values = series_sin(arr)
```
## Usage
### Syntax
```kusto theme={null}
series_sin(arr)
```
### Parameters
| Parameter | Type | Description |
| --------- | ------- | --------------------------- |
| `arr` | dynamic | An array of numeric values. |
### Returns
A dynamic array where each element is the sine of the corresponding input element.
## Use case examples
You can use `series_sin` to transform request durations into trigonometric values for advanced analysis, such as periodicity detection.
**Query**
```kusto theme={null}
['sample-http-logs']
| summarize arr = make_list(req_duration_ms, 10)
| extend sin_arr = series_sin(arr)
```
[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B'sample-http-logs'%5D%20%7C%20summarize%20arr%20%3D%20make_list\(req_duration_ms%2C%2010\)%20%7C%20extend%20sin_arr%20%3D%20series_sin\(arr\)%22%7D)
**Output**
| arr | sin\_arr |
| --------------------- | ---------------------------- |
| \[120, 250, 500, 750] | \[−0.58, −0.97, −0.52, 0.94] |
This query collects a sample of request durations and applies `series_sin` to generate a transformed series for analysis.
You can use `series_sin` to apply trigonometric transformation to span durations for modeling or feature extraction.
**Query**
```kusto theme={null}
['otel-demo-traces']
| summarize arr = make_list(toint(duration), 10) by ['service.name']
| extend sin_arr = series_sin(arr)
```
[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B'otel-demo-traces'%5D%20%7C%20summarize%20arr%20%3D%20make_list\(toint\(duration\)%2C%2010\)%20by%20%5B'service.name'%5D%20%7C%20extend%20sin_arr%20%3D%20series_sin\(arr\)%22%7D)
**Output**
| service.name | arr | sin\_arr |
| ------------ | ---------------- | --------------------- |
| frontend | \[200, 400, 600] | \[0.91, −0.73, −0.28] |
This query groups spans by service, aggregates durations into arrays, and transforms them using `series_sin`.
You can use `series_sin` to apply mathematical transformations to response times in security-related traffic to detect unusual patterns.
**Query**
```kusto theme={null}
['sample-http-logs']
| summarize arr = make_list(req_duration_ms, 10) by ['geo.country']
| extend sin_arr = series_sin(arr)
```
[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B'sample-http-logs'%5D%20%7C%20summarize%20arr%20%3D%20make_list\(req_duration_ms%2C%2010\)%20by%20%5B'geo.country'%5D%20%7C%20extend%20sin_arr%20%3D%20series_sin\(arr\)%22%7D)
**Output**
| geo.country | arr | sin\_arr |
| ----------- | ---------------- | ---------------------- |
| US | \[180, 360, 540] | \[−0.80, −0.99, −0.84] |
This query filters failed requests (`403`) by country, aggregates durations, and applies `series_sin` to identify periodic anomalies.
## List of related functions
* [series\_abs](/apl/scalar-functions/time-series/series-abs): Returns the absolute value of each element in an array. Use it to normalize negative values in arrays.
* [series\_acos](/apl/scalar-functions/time-series/series-acos): Computes the arccosine of each element in an array. Use when you want the inverse cosine.
* [series\_atan](/apl/scalar-functions/time-series/series-atan): Computes the arctangent of each element in an array. Use when you want the inverse tangent.
* [series\_cos](/apl/scalar-functions/time-series/series-cos): Returns the cosine of each element in an array. Use it when analyzing cyclical data with a phase shift.
* [series\_tan](/apl/scalar-functions/time-series/series-tan): Returns the tangent of each element in an array. Use it when you want to transform arrays with tangent-based periodicity.