The series_acos function computes the arc cosine (inverse cosine) for each numeric element in a dynamic array. The output is another dynamic array where each value is transformed by the arc cosine function. You use series_acos when you want to apply trigonometric analysis over time series or other numeric array data. This is useful in cases where your data is stored as arrays, such as time-binned metrics, periodic request patterns, or wave-like behaviors in telemetry data.

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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.

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Usage

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Syntax

series_acos(array)

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Parameters

ParameterTypeDescription
arraydynamicA dynamic array of numeric values where each element is between -1 and 1.

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Returns

A dynamic array of the same length as the input where each element is the arc cosine of the corresponding input element. The result values are in radians, in the range [0, π].

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Use case examples

You can analyze the periodicity of request durations. By applying series_acos to normalized values, you reveal inverse cosine transformations that are useful in signal-style analysis of request patterns.Query
['sample-http-logs']
| summarize durations = make_list(req_duration_ms, 100) by id
| extend normalized = series_acos(durations)
Run in PlaygroundOutput
iddurationsnormalized
U123[100, 200, 300, 400][1.47, 1.37, 1.27, 1.16]
The query computes request duration arrays for each user, normalizes them, and applies the inverse cosine function element-wise.
  • series_asin: Applies the arc sine function element-wise to array values. Use this when you need the inverse sine instead of the inverse cosine.
  • series_atan: Applies the arc tangent function element-wise to array values. Use this when analyzing angular relationships that use tangent ratios.