# 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.

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 / operator.

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 New formula Single row formula round(radians(X), 3) 'rX'

Hyperbolic Sine:

 Transformation Name New formula Single row formula round(sinh(rX), 3) 'SINHrX'

Hyperbolic Cosine:

 Transformation Name New formula Single row formula round(cosh(rX), 3) 'COSHrX'

Hyperbolic Tangent:

 Transformation Name New formula Single row formula round(tanh(rX), 3) 'TANHrX'

Hyperbolic Cotangent:

 Transformation Name New formula Single row formula round(divide(1, tanh(rX)), 3) 'COTHrX'

Hyperbolic Secant:

 Transformation Name New formula Single row formula round(divide(1, cosh(rX)), 3) 'SECHrX'

Hyperbolic Cosecant:

 Transformation Name New formula Single row formula round(divide(1, sinh(rX)), 3) '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