Contents:
This example illustrates how to apply the inverse trigonometric (Arc) functions to your transformations.
NOTE: These functions are valid over specific ranges.
- Arcsine. See ASIN Function.
- Arccosine. See ACOS Function
- Arctangent. See ATAN Function.
- 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. For more information, see ASIN Function.
| 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. For more information, see ACOS 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. For more information, see ATAN Function.
| 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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