For input values between -1 and 1 inclusive, this function returns the angle in radians whose cosine value is the input. This function is the inverse of the cosine function. The value can be a Decimal or Integer literal or a reference to a column containing numeric values.
NOTE: While this function returns values outside of the range -1 <= x <= 1, those values are not considered valid.
For more information on the cosine function, see COS Function.
Arc secant:
The arc secant function is computed as follows:
| Input Range | Output computation |
|---|---|
| x<=-1 | acos(1/x) |
| x>=1 | acos(1/x) |
| -1<x<1 | Not valid |
Wrangle vs. SQL: This function is part of Wrangle, a proprietary data transformation language. Wrangle is not SQL. For more information, see Wrangle Language.
Basic Usage
Numeric literal example:
acos(0.5)
Output: Returns the computation of the arc cosine of 0.5. Output value is in radians.
Column reference example:
acos(X)
Output: Returns the arc cosine of the values in X column.
Syntax and Arguments
acos(numeric_value)
| Argument | Required? | Data Type | Description |
|---|---|---|---|
| numeric_value | Y | string, decimal, or integer | Name of column, Decimal or Integer literal, or function returning those types to apply to the function |
For more information on syntax standards, see Language Documentation Syntax Notes.
numeric_value
Name of the column, Integer or Decimal literal, or function returning that data type to apply to the function.
- Missing input values generate missing results.
- Literal numeric values should not be quoted. Quoted values are treated as strings.
- Multiple columns and wildcards are not supported.
Usage Notes:
| Required? | Data Type | Example Value |
|---|---|---|
| Yes | String (column reference) or Integer or Decimal literal | 0.5 |
Tip: For additional examples, see Common Tasks.
Examples
Example - Trigonometry Arc functions
Functions:
| Item | Description |
|---|---|
| ASIN Function | For input values between -1 and 1 inclusive, this function returns the angle in radians whose sine value is the input. This function is the inverse of the sine function. The value can be a Decimal or Integer literal or a reference to a column containing numeric values. |
| ACOS Function | For input values between -1 and 1 inclusive, this function returns the angle in radians whose cosine value is the input. This function is the inverse of the cosine function. The value can be a Decimal or Integer literal or a reference to a column containing numeric values. |
| ATAN Function | For input values between -1 and 1 inclusive, this function returns the angle in radians whose tangent value is the input. This function is the inverse of the tangent function. The value can be a Decimal or Integer literal or a reference to a column containing numeric values. |
Also:
| Item | Description |
|---|---|
| ROUND Function | Rounds input value to the nearest integer. Input can be an Integer, a Decimal, a column reference, or an expression. Optional second argument can be used to specify the number of digits to which to round. |
| DEGREES Function | Computes the degrees of an input value measuring the radians of an angle. The value can be a Decimal or Integer literal or a reference to a column containing numeric values. |
NOTE: These functions are valid over specific ranges.
The following functions are computed using the above functions.
- Arccotangent. Computed using ATAN function. See below.
- Arcsecant. Computed using ACOS function. See below.
- Arccosecant. Computed using ASIN function. See below.
Source:
In the following sample, input values are in radians. In this example, all values are rounded to two decimals for clarity.
| Y |
|---|
| -1.00 |
| -0.75 |
| -0.50 |
| 0.00 |
| 0.50 |
| 0.75 |
| 1.00 |
Transformation:
Arcsine:
Valid over the range (-1 <= Y <= 1)
| Transformation Name | New formula |
|---|---|
| Parameter: Formula type | Single row formula |
| Parameter: Formula | round(degrees(asin(Y)), 2) |
| Parameter: New column name | 'asinY' |
Arccosine:
Valid over the range (-1 <= Y <= 1)
| Transformation Name | New formula |
|---|---|
| Parameter: Formula type | Single row formula |
| Parameter: Formula | round(degrees(acos(Y)), 2) |
| Parameter: New column name | 'acosY' |
Arctangent:
Valid over the range (-1 <= Y <= 1)
| Transformation Name | New formula |
|---|---|
| Parameter: Formula type | Single row formula |
| Parameter: Formula | round(degrees(atan(Y)), 2) |
| Parameter: New column name | 'atanY' |
Arccosecant:
This function is valid over a set of ranged inputs, so you can use a conditional column for the computation.
| Transformation Name | Conditional column |
|---|---|
| Parameter: Condition type | if...then...else |
| Parameter: If | (Y <= -1) || (Y >= 1) |
| Parameter: Then | round(degrees(asin(divide(1, Y))), 2) |
| Parameter: New column name | 'acscY' |
Arcsecant:
Same set of ranged inputs apply to this function.
| Transformation Name | Conditional column |
|---|---|
| Parameter: Condition type | if...then...else |
| Parameter: If | (Y <= -1) || (Y >= 1) |
| Parameter: Then | round(degrees(acos(divide(1, Y))), 2) |
| Parameter: New column name | 'asecY' |
Arccotangent:
For this function, the two different ranges of inputs have different computations, so an else condition is added to the transformation.
| Transformation Name | Conditional column |
|---|---|
| Parameter: Condition type | if...then...else |
| Parameter: If | Y > 0 |
| Parameter: Then | round(degrees(atan(divide(1, Y))), 2) |
| Parameter: Else | round(degrees(atan(divide(1, Y)) + pi()), 2) |
| Parameter: New column name | 'acotY' |
Results:
| Y | acotY | asecY | acscY | atanY | acosY | asinY |
|---|---|---|---|---|---|---|
| -1.00 | -41.86 | 180.00 | -90.00 | -45.00 | 180.00 | -90.00 |
| -0.75 | -49.99 | null | null | -37.00 | 139.00 | -49.00 |
| -0.50 | -60.29 | null | null | -27.00 | 120.00 | -30.00 |
| 0.00 | null | null | null | 0.00 | 90.00 | 0.00 |
| 0.50 | 63.44 | null | null | 27.00 | 60.00 | 30.00 |
| 0.75 | 53.13 | null | null | 37.00 | 41.00 | 49.00 |
| 1.00 | 45.00 | 0.00 | 90.00 | 45.00 | 0.00 | 90.00 |
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