EXAMPLE - Trigonometry Hyperbolic Functions
This example illustrates how to apply hyperbolic trigonometric functions to your transformations. All of the functions take inputs in radians.
Functions:
Item | Description |
|---|---|
SINH Function | Computes the hyperbolic sine 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. |
COSH Function | Computes the hyperbolic cosine 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. |
TANH Function | Computes the hyperbolic tangent 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. |
The following functions can be computed based on the inverse of the above functions:
Hyperbolic Cotangent. Computed as 1/TANH.
Hyperbolic Secant. Computed as 1/COSH.
Hyperbolic Cosecant. Computed as 1/SINH.
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. |
RADIANS Function | Computes the radians of an input value measuring degrees of an angle. The value can be a Decimal or Integer literal or a reference to a column containing numeric values. |
DIVIDE Function | Returns the value of dividing the first argument by the second argument. Equivalent to the |
Source:
In the following sample, input values are in degrees:
X |
|---|
-30 |
0 |
30 |
45 |
60 |
90 |
120 |
135 |
180 |
Transformation:
In this example, all values are rounded to three decimals for clarity.
First, the above values in degrees must be converted to radians.
Transformation Name | |
|---|---|
Parameter: Formula type | Single row formula |
Parameter: Formula | round(radians(X), 3) |
Parameter: New column name | 'rX' |
Hyperbolic Sine:
Transformation Name | |
|---|---|
Parameter: Formula type | Single row formula |
Parameter: Formula | round(sinh(rX), 3) |
Parameter: New column name | 'SINHrX' |
Hyperbolic Cosine:
Transformation Name | |
|---|---|
Parameter: Formula type | Single row formula |
Parameter: Formula | round(cosh(rX), 3) |
Parameter: New column name | 'COSHrX' |
Hyperbolic Tangent:
Transformation Name | |
|---|---|
Parameter: Formula type | Single row formula |
Parameter: Formula | round(tanh(rX), 3) |
Parameter: New column name | 'TANHrX' |
Hyperbolic Cotangent:
Transformation Name | |
|---|---|
Parameter: Formula type | Single row formula |
Parameter: Formula | round(divide(1, tanh(rX)), 3) |
Parameter: New column name | 'COTHrX' |
Hyperbolic Secant:
Transformation Name | |
|---|---|
Parameter: Formula type | Single row formula |
Parameter: Formula | round(divide(1, cosh(rX)), 3) |
Parameter: New column name | 'SECHrX' |
Hyperbolic Cosecant:
Transformation Name | |
|---|---|
Parameter: Formula type | Single row formula |
Parameter: Formula | round(divide(1, sinh(rX)), 3) |
Parameter: New column name | 'CSCHrX' |
Results:
X | rX | TANHrX | COTHrX | COSHrX | SECHrX | SINHrX | CSCHrX |
|---|---|---|---|---|---|---|---|
-30 | -0.524 | -0.481 | -2.079 | 1.14 | 0.877 | -0.548 | -1.825 |
0 | 0 | 0 | null | 1 | 1 | 0 | null |
30 | 0.524 | 0.481 | 2.079 | 1.14 | 0.877 | 0.548 | 1.825 |
45 | 0.785 | 0.656 | 1.524 | 1.324 | 0.755 | 0.868 | 1.152 |
60 | 1.047 | 0.781 | 1.28 | 1.6 | 0.625 | 1.249 | 0.801 |
90 | 1.571 | 0.917 | 1.091 | 2.51 | 0.398 | 2.302 | 0.434 |
120 | 2.094 | 0.97 | 1.031 | 4.12 | 0.243 | 3.997 | 0.25 |
135 | 2.356 | 0.982 | 1.018 | 5.322 | 0.188 | 5.227 | 0.191 |
180 | 3.142 | 0.996 | 1.004 | 11.597 | 0.086 | 11.553 | 0.087 |