cot ↗

Use the cot() function to calculate the cotangent of a numeric value specified in radians. The cotangent is the reciprocal of the tangent function.

Syntax

cot(<numeric_expression>)

Parameters

Name Type Required Description
numeric_expression integer, float Yes The angle in radians for which to calculate the cotangent. The value must not be zero or a multiple of π.

Returns

Type: float

Description: The cot() function returns the cotangent of the input angle, which is equivalent to cos(x) / sin(x) or 1 / tan(x). If the input is null, the function returns null.

Usage notes

  • Input type: XQL doesn't support NaN or infinite values as input and these value types also can not be returned.
  • Valid Input Range: The cot() function accepts any real number except values where sin(x) = 0 (i.e., multiples of π), where the cotangent is undefined.
  • Undefined Values: At x = 0 and multiples of π, the function returns infinity, NaN, or null since the cotangent is undefined at these points.
  • Null Handling: If the input expression is null, the function returns null.
  • Relationship: cot(x) = 1 / tan(x) = cos(x) / sin(x).
  • Common Use Cases: This function is typically used within the alter stage for trigonometric calculations, geometric analysis, and engineering computations.

Examples

Example 1: Calculate cotangent of literal values

Goal: Calculate the cotangent for specific radian values to verify known mathematical results.

XQL code:

dataset = xdr_data
| limit 1
| alter result1 = cot(divide(pi(), 4)), result2 = cot(divide(pi(), 2)), result3 = cot(1)
| fields result1, result2, result3

Explanation: You use cot() on three different radian values. cot(π/4) returns 1.0 (since tan(π/4) = 1), cot(π/2) returns approximately 0.0 (since tan(π/2) approaches infinity), and cot(1) returns approximately 0.6421.

Output:

RESULT1 RESULT2 RESULT3
1.0 0.0 0.64209

Example 2: Calculate cotangent from a field value

Goal: Calculate the cotangent of values stored in a dataset field, filtering out values near zero.

XQL code:

config timeframe = 1d
| dataset = sample_xql_raw
| filter numeric_value != 0
| alter cot_val = cot(numeric_value)
| fields event_id, numeric_value, cot_val
| limit 3

Explanation: This query filters out zero values (where cotangent is undefined), then computes the cotangent for each remaining value in the numeric_value field.

Output:

EVENT_ID NUMERIC_VALUE COT_VAL
101 0.5 1.83049
102 1.0 0.64209
103 2.0 -0.45766

Example 3: Verify cotangent as reciprocal of tangent

Goal: Demonstrate that cot(x) equals 1 / tan(x) by computing both and comparing.

XQL code:

config timeframe = 1d
| dataset = sample_xql_raw
| filter numeric_value != 0
| alter cot_val = cot(numeric_value)
| alter reciprocal_tan = divide(1, tan(numeric_value))
| fields event_id, numeric_value, cot_val, reciprocal_tan
| limit 3

Explanation: This query computes both cot(numeric_value) and 1 / tan(numeric_value) to verify they produce the same result, confirming the mathematical identity cot(x) = 1 / tan(x).

Output:

EVENT_ID NUMERIC_VALUE COT_VAL RECIPROCAL_TAN
101 0.5 1.83049 1.83049
102 1.0 0.64209 0.64209
103 2.0 -0.45766 -0.45766