EXAMPLE - Trigonometry Hyperbolic Arc Functions
This example illustrates how to apply inverse (arc) hyperbolic functions to your transformations.
Functions:
Item | Description |
|---|---|
ASINH Function | Computes the arcsine of an input value for a hyperbolic angle measured in radians. The value can be a Decimal or Integer literal or a reference to a column containing numeric values. |
ACOSH Function | Computes the arccosine of an input value for a hyperbolic angle measured in radians. The value can be a Decimal or Integer literal or a reference to a column containing numeric values. |
ATANH Function | Computes the arctangent of an input value for a hyperbolic angle measured in radians. 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. |
NULL Function | The |
Source:
In the following sample, input values are in radians. In this example, all values are rounded to two decimals for clarity.
Y |
|---|
-4.00 |
-3.00 |
-2.00 |
-1.00 |
-0.75 |
-0.50 |
0.00 |
0.50 |
0.75 |
1.00 |
2.00 |
3.00 |
4.00 |
Transformation:
The following transformations include checks for the valid ranges for input values.
Hyperbolic arcsine:
Transformation Name |
|
|---|---|
Parameter: Formula type | Single row formula |
Parameter: Formula | round(degrees(asinh(Y)), 2) |
Parameter: New column name | 'asinhY' |
Hyperbolic arccosine:
Valid over the range (y > 1)
Transformation Name |
|
|---|---|
Parameter: Formula type | Single row formula |
Parameter: Formula | if(Y>1,round(degrees(acosh(Y)), 2),null()) |
Parameter: New column name | 'acoshY' |
Hyperbolic arctangent:
Valid over the range (-1 < y < 1)
Transformation Name |
|
|---|---|
Parameter: Formula type | Single row formula |
Parameter: Formula | if(abs(y)<1,round(degrees(atanh(Y)), 2),null()) |
Parameter: New column name | 'atanhY' |
Results:
Y | atanhY | acoshY | asinhY |
|---|---|---|---|
-4 | null | null | -120.02 |
-3 | null | null | -104.19 |
-2 | null | null | -82.71 |
-1.5 | null | null | -68.45 |
-1 | null | null | -50.5 |
-0.75 | -55.75 | null | -39.71 |
-0.5 | -31.47 | null | -27.57 |
0 | 0 | null | 0 |
0.5 | 31.47 | null | 27.57 |
0.75 | 55.75 | null | 39.71 |
1 | null | null | 50.5 |
1.5 | null | 55.14 | 68.45 |
2 | null | 75.46 | 82.71 |
3 | null | 101 | 104.19 |
4 | null | 118.23 | 120.02 |