9.5 Math object

Description

You can apply many mathematical operations (trigonometry, logarithmize, square root, rounding, ...) with the Math object.

List of methods/properties

Name	Type	Short description
Pi	Property	Returns Ludolph's number (π = 3,141592653589...)
E	Property	Returns Euler's number (e = 2,718281828...)
Abs	Method	Returns the absolute value of a number
Sin	Method	Calculates the sine of an angle
Cos	Method	Calculates the cosine of an angle
Tan	Method	Calculates the tangent of an angle
Cot	Method	Calculates the cotangent of an angle
Sec	Method	Calculates the sekant of an angle
Csc	Method	Calculates the cosekant of an angle
ASin	Method	Calculates the angle of a sine
ACos	Method	Calculates the angle of a cosine
ATan	Method	Calculates the angle of a tangent
ACot	Method	Calculates the angle of a cotangent
ASec	Method	Calculates the angle of a sekant
ACsc	Method	Calculates the angle of a cosekant
SinH	Method	Calculates the hyperbolic sine
CosH	Method	Calculates the hyperbolic cosine
TanH	Method	Calculates the hyperbolic tangent
CotH	Method	Calculates the hyperbolic cotangent
SecH	Method	Calculates the hyperbolic sekant
CscH	Method	Calculates the hyperbolic cosekant
ASinH	Method	Calculates the inverted hyperbolic sine
ACosH	Method	Calculates the inverted hyperbolic cosine
ATanH	Method	Calculates the inverted hyperbolic tangent
ACotH	Method	Calculates the inverted hyperbolic cotangent
ASecH	Method	Calculates the inverted hyperbolic sekant
ACscH	Method	Calculates the inverted hyperbolic cosekant
Power	Method	Exponentiates a base with an exponent
Log	Method	Calculates the logarithm to any base
Lg	Method	Calculates the decade logarithm (base: 10)
Ln	Method	Calculates the natural logarithm (base: e = 2,718281828...)
Lb	Method	Calculates the binary logarithm (base: 2)
Sqrt	Method	Calculates the square root of a number
Cmp	Method	Compares two values
Exp	Method	Exponates the number 10 with an exponent
Round	Method	Rounds a number halfway away from zero
RoundUp	Method	Rounds a number in direction to +∞
RoundDown	Method	Rounds a number in direction to -∞
Int	Method	Cuts the decimal places of a number
Scale	Method	Cuts the integer places of a number

Pi

Description

This property represents Ludolph's number (π = 3,141592653589...).

Syntax

Math.Pi

Data type

Double

Type

Property, read-only

Example

1
2

$
f[1] = Math.Pi

f[1] whould be at end: 3,141592653589...

E

Description

This property represents Euler's number (e = 2,718281828...).

Syntax

Math.E

Data type

Double

Type

Property, read-only

Example

1
2

$
f[1] = Math.E

f[1] whould be at end: 2,718281828...

Abs

Description

Returns the absolute value of a number (this means the leading sign will always be plus).

Syntax

Math.Abs(Number)

Return value

Double

Type

Method

Parameter: Number

Description

The number whose absolute value shall be returned.

Data type

Double

Example

1
2

$
f[1] = Math.Abs(-2)

f[1] whould be at end: 2

Calculates the sine of an angle (= opposite leg / hypotenuse). You can specify the angle in one of four angle formats: DEG, RAD, GRAD and RPG. These names are specified as constants and can be used directly as parameter. DEG stands for degree and means that a full circle has 360 angle units. RAD stands for radiant and means that the radian measure (a full circle has π angle units) is used. GRAD stands for grad and means that a full circle has 400 angle units. RPG is a RPG-Maker specific format and means that a full circle has 256 angle units.

Syntax

Math.Sin(Angle, Format)

Return value

Double

Type

Method

Parameter: Angle

Description

The angle which shall be calculated.

Data type

Double

Parameter: Format

Description

The current format of the angle.

Data type

Dword

Range

1 to 4 (Constants: DEG, RAD, GRAD and RPG)

Example

1
2

$
f[1] = Math.Sin(90, DEG)

f[1] whould be at end: 1

Cos

Description

Calculates the cosine of an angle (= adjacent leg / hypotenuse). (For a description of the angle formats see Sin method)

Syntax

Math.Cos(Angle, Format)

Return value

Double

Type

Method

Parameter: Angle

Description

The angle which shall be calculated.

Data type

Double

Parameter: Format

Description

The current format of the angle.

Data type

Dword

Range

1 to 4 (Constants: DEG, RAD, GRAD and RPG)

Example

1
2

$
f[1] = Math.Cos(Math.Pi, RAD)

f[1] whould be at end: -1

Tan

Description

Calculates the tangent of an angle (= opposite leg / adjacent leg). (For a description of the angle formats see Sin method)

Syntax

Math.Tan(Angle, Format)

Return value

Double

Type

Method

Parameter: Angle

Description

The angle which shall be calculated.

Data type

Double

Parameter: Format

Description

The current format of the angle.

Data type

Dword

Range

1 to 4 (Constants: DEG, RAD, GRAD and RPG)

Example

1
2

$
f[1] = Math.Tan(50, GRAD)

f[1] whould be at end: 1

Cot

Description

Calculates the cotangent of an angle (= adjacent leg / opposite leg). (For a description of the angle formats see Sin method)

Syntax

Math.Cot(Angle, Format)

Return value

Double

Type

Method

Parameter: Angle

Description

The angle which shall be calculated.

Data type

Double

Parameter: Format

Description

The current format of the angle.

Data type

Dword

Range

1 to 4 (Constants: DEG, RAD, GRAD and RPG)

Example

1
2

$
f[1] = Math.Cot(96, RPG)

f[1] whould be at end: -1

Sec

Description

Calculates the sekant of an angle (= hypotenuse / adjacent leg). (For a description of the angle formats see Sin method)

Syntax

Math.Sec(Angle, Format)

Return value

Double

Type

Method

Parameter: Angle

Description

The angle which shall be calculated.

Data type

Double

Parameter: Format

Description

The current format of the angle.

Data type

Dword

Range

1 to 4 (Constants: DEG, RAD, GRAD and RPG)

Example

1
2

$
f[1] = Math.Sec(45, DEG)

f[1] whould be at end: 1,414213562373...

Csc

Description

Calculates the cosekant of an angle (= hypotenuse / opposite leg). (For a description of the angle formats see Sin method)

Syntax

Math.Csc(Angle, Format)

Return value

Double

Type

Method

Parameter: Angle

Description

The angle which shall be calculated.

Data type

Double

Parameter: Format

Description

The current format of the angle.

Data type

Dword

Range

1 to 4 (Constants: DEG, RAD, GRAD and RPG)

Example

1
2

$
f[1] = Math.Csc(30, DEG)

f[1] whould be at end: 2

ASin

Description

Calculates the angle from a sine (= arc sine). (For a description of the angle formats see Sin method)

Syntax

Math.Asin(Sine, Format)

Return value

Double

Type

Method

Parameter: Sine

Description

The sine value.

Data type

Double

Parameter: Format

Description

The target angle format.

Data type

Dword

Range

1 to 4 (Constants: DEG, RAD, GRAD and RPG)

Example

1
2

$
f[1] = Math.Asin(30, DEG)

f[1] whould be at end: 30

ACos

Description

Calculates the angle from a cosine (arc cosine). (For a description of the angle formats see Sin method)

Syntax

Math.Acos(Cosine, Format)

Return value

Double

Type

Method

Parameter: Cosine

Description

The cosine value.

Data type

Double

Parameter: Format

Description

The target angle format.

Data type

Dword

Range

1 to 4 (Constants: DEG, RAD, GRAD and RPG)

Example

1
2

$
f[1] = Math.Acos(1, GRAD)

f[1] whould be at end: 0

ATan

Description

Calculates the angle from a tangent (= arc tangent). (For a description of the angle formats see Sin method)

Syntax

Math.Atan(Tangent, Format)

Return value

Double

Type

Method

Parameter: Tangent

Description

The tangent value.

Data type

Double

Parameter: Format

Description

The target angle format.

Data type

Dword

Range

1 to 4 (Constants: DEG, RAD, GRAD and RPG)

Example

1
2

$
f[1] = Math.Atan(1, DEG)

f[1] whould be at end: 45

ACot

Description

Calculates the angle from a cotangent (= arc cotangent). (For a description of the angle formats see Sin method)

Syntax

Math.Acot(Cotangent, Format)

Return value

Double

Type

Method

Parameter: Cotangent

Description

The cotangent value.

Data type

Double

Parameter: Format

Description

The target angle format.

Data type

Dword

Range

1 to 4 (Constants: DEG, RAD, GRAD and RPG)

Example

1
2

$
f[1] = Math.Acot(-1, DEG)

f[1] whould be at end: 135 (= -45)

ASec

Description

Calculates the angle from a sekant (= arc sekant). (For a description of the angle formats see Sin method)

Syntax

Math.Asec(Sekant, Format)

Return value

Double

Type

Method

Parameter: Sekant

Description

The sekant value.

Data type

Double

Parameter: Format

Description

The target angle format.

Data type

Dword

Range

1 to 4 (Constants: DEG, RAD, GRAD and RPG)

Example

1
2

$
f[1] = Math.Asec(2, DEG)

f[1] whould be at end: 60

ACsc

Description

Calculates the angle from a cosekant (= arc cosekant). (For a description of the angle formats see Sin method)

Syntax

Math.Acsc(Cosekant, Format)

Return value

Double

Type

Method

Parameter: Cosekant

Description

The cosekant value.

Data type

Double

Parameter: Format

Description

The target angle format.

Data type

Dword

Range

1 to 4 (Constants: DEG, RAD, GRAD and RPG)

Example

1
2

$
f[1] = Math.Acsc(1, RPG)

f[1] whould be at end: 64

SinH

Description

Calculates the hyperbolic sine.

Syntax

Math.Sinh(Number)

Return value

Double

Type

Method

Parameter: Number

Description

The number which shall be calculated.

Data type

Double

Example

1
2

$
f[1] = Math.Sinh(f[2])

CosH

Description

Calculates the hyperbolic cosine.

Syntax

Math.Cosh(Number)

Return value

Double

Type

Method

Parameter: Number

Description

The number which shall be calculated.

Data type

Double

Example

1
2

$
f[1] = Math.Cosh(f[2])

TanH

Description

Calculates the hyperbolic tangent.

Syntax

Math.Tanh(Number)

Return value

Double

Type

Method

Parameter: Number

Description

The number which shall be calculated.

Data type

Double

Example

1
2

$
f[1] = Math.Tanh(f[2])

CotH

Description

Calculates the hyperbolic cotangent.

Syntax

Math.Coth(Number)

Return value

Double

Type

Method

Parameter: Number

Description

The number which shall be calculated.

Data type

Double

Example

1
2

$
f[1] = Math.Coth(f[2])

SecH

Description

Calculates the hyperbolic sekant.

Syntax

Math.Sech(Number)

Return value

Double

Type

Method

Parameter: Number

Description

The number which shall be calculated.

Data type

Double

Example

1
2

$
f[1] = Math.Sech(f[2])

CscH

Description

Calculates the hyperbolic cotangent.

Syntax

Math.Csch(Number)

Return value

Double

Type

Method

Parameter: Number

Description

The number which shall be calculated.

Data type

Double

Example

1
2

$
f[1] = Math.Csch(f[2])

ASinH

Description

Calculates the inverted hyperbolic sine (area hyperbolic sine).

Syntax

Math.Asinh(Number)

Return value

Double

Type

Method

Parameter: Number

Description

The number which shall be calculated.

Data type

Double

Example

1
2

$
f[1] = Math.Asinh(f[2])

ACosH

Description

Calculates the inverted hyperbolic cosine (area hyperbolic cosine).

Syntax

Math.Acosh(Number)

Return value

Double

Type

Method

Parameter: Number

Description

The number which shall be calculated.

Data type

Double

Example

1
2

$
f[1] = Math.Acosh(f[2])

ATanH

Description

Calculates the inverted hyperbolic tangent (area hyperbolic tangent).

Syntax

Math.Atanh(Number)

Return value

Double

Type

Method

Parameter: Number

Description

The number which shall be calculated.

Data type

Double

Example

1
2

$
f[1] = Math.Atanh(f[2])

ACotH

Description

Calculates the inverted hyperbolic cotangent (area hyperbolic cotangent).

Syntax

Math.Acoth(Number)

Return value

Double

Type

Method

Parameter: Number

Description

The number which shall be calculated.

Data type

Double

Example

1
2

$
f[1] = Math.Acoth(f[2])

ASecH

Description

Calculates the inverted hyperbolic sekant (area hyperbolic sekant).

Syntax

Math.Asech(Number)

Return value

Double

Type

Method

Parameter: Number

Description

The number which shall be calculated.

Data type

Double

Example

1
2

$
f[1] = Math.Asech(f[2])

ACscH

Description

Calculates the inverted hyperbolic cosekant (area hyperbolic cosekant).

Syntax

Math.Acsch(Number)

Return value

Double

Type

Method

Parameter: Number

Description

The number which shall be calculated.

Data type

Double

Example

1
2

$
f[1] = Math.Acsch(f[2])

Power

Description

Exponentiates the base with the exponent.

Syntax

Math.Power(Base, Exponent)

Return value

Double

Type

Method

Parameter: Base

Description

The base value.

Data type

Double

Parameter: Exponent

Description

The exponent value.

Data type

Double

Example

1
2

$
f[1] = Math.Power(3, 4)

f[1] whould be at end: 81 (= 3 * 3 * 3 * 3)

Log

Description

Calculates the logarithm of any base.

Syntax

Math.Log(Number, Base)

Return value

Double

Type

Method

Parameter: Number

Description

The number whose logarithm shall be calculated.

Data type

Double

Parameter: Base

Description

The base of the logarithm.

Data type

Double

Example

1
2

$
f[1] = Math.Log(25, 5)

f[1] whould be at end: 2

Lg

Description

Calculates the decade logarithm (the base is 10).

Syntax

Math.Lg(Number)

Return value

Double

Type

Method

Parameter: Number

Description

The number whose logarithm shall be calculated.

Data type

Double

Example

1
2

$
f[1] = Math.Lg(1000)

f[1] whould be at end: 3

Ln

Description

Calculates the natural logarith (the base is Euler's number).

Syntax

Math.Ln(Number)

Return value

Double

Type

Method

Parameter: Number

Description

The number whose logarithm shall be calculated.

Data type

Double

Example

1
2

$
f[1] = Math.Ln(1 / Math.E)

f[1] whould be at end: -1

Lb

Description

Calculates the binary logarithm (the base is 2).

Syntax

Math.Lb(Number)

Return value

Double

Type

Method

Parameter: Number

Description

The number whose logarithm shall be calculated.

Data type

Double

Example

1
2

$
f[1] = Math.Lb(256)

f[1] whould be at end: 8

Sqrt

Description

Calculates the square root of a number.

Syntax

Math.Sqrt(Number)

Return value

Double

Type

Method

Parameter: Number

Description

The number whose square root shall be calculated.

Data type

Double

Example

1
2

$
f[1] = Math.Sqrt(10000)

f[1] whould be at end: 100

Cmp

Description

Compares two numbers. If the first number is smaller than the second number then the result will be < 0. If the first number is greater than the second number then the result will be > 0. If both numbers are the same then the result will be = 0.

Syntax

Math.Cmp(Number1, Number2)

Return value

Dword

Type

Method

Parameter: Number1

Description

The first number to compare.

Data type

Double

Parameter: Number2

Description

The second number to compare.

Data type

Double

Example

1
2

$
d[1] = Math.Cmp(1, 2)

f[1] whould be at end: -1

Exp

Description

Exponentiates the number 10 with the specified number.

Syntax

Math.Exp(Number)

Return value

Double

Type

Method

Parameter: Number

Description

The exponent for the number 10.

Data type

Double

Example

1
2

$
f[1] = Math.Exp(5)

f[1] whould be at end: 100000

Round

Description

Rounds a number halfway away from zero (this means 5 to 9 will be rounded up) to the specified place. If you specify 0 as place then the decimal part will be rounded to the integer part. If you specify a positive number as place then you round to that decimal place. If you specify a negative number as place then you round to that integer place.

Syntax

Math.Round(Number, Place)

Return value

Double

Type

Method

Parameter: Number

Description

The number which shall be rounded.

Data type

Double

Parameter: Place

Description

The place which shall be rounded (measured from the decimal separator).

Data type

Dword

Example

1
2

$
f[1] = Math.Round(3.345, 2)

f[1] whould be at end: 3.35

RoundUp

Description

Rounds a number into the direction of +∞ (this means from 1 to 9 will be rounded up) to the specified place. If you specify 0 as place then the decimal part will be rounded to the integer part. If you specify a positive number as place then you round to that decimal place. If you specify a negative number as place then you round to that integer place.

Syntax

Math.RoundUp(Number, Place)

Return value

Double

Type

Method

Parameter: Number

Description

The number which shall be rounded.

Data type

Double

Parameter: Place

Description

The place which shall be rounded (measured from the decimal separator).

Data type

Dword

Example

1
2

$
f[1] = Math.RoundUp(-300.7, 0)

f[1] whould be at end: -300 (if you round into the direction of +∞ then the result will always be more positive)

RoundDown

Description

Rounds a number into the direction of -∞ (this means from 1 to 9 will be rounded down) to the specified place. If you specify 0 as place then the decimal part will be rounded to the integer part. If you specify a positive number as place then you round to that decimal place. If you specify a negative number as place then you round to that integer place.

Syntax

Math.RoundDown(Number, Place)

Return value

Double

Type

Method

Parameter: Number

Description

The number which shall be rounded.

Data type

Double

Parameter: Place

Description

The place which shall be rounded (measured from the decimal separator).

Data type

Dword

Example

1
2

$
f[1] = Math.RoundDown(592.001, -2)

f[1] whould be at end: 500

Int

Description

Cuts the decimal part of a number.

Syntax

Math.Int(Number)

Return value

Double

Type

Method

Parameter: Number

Description

The number whose decimal part shall be removed.

Data type

Double

Example

1
2

$
f[1] = Math.Int(123.456)

f[1] whould be at end: 123

Scale

Description

Cuts the integer part of a number.

Syntax

Math.Scale(Number)

Return value

Double

Type

Method

Parameter: Number

Description

The number whose integer part shall be removed.

Data type

Double

Example

1
2

$
f[1] = Math.Scale(123.456)

f[1] whould be at end: 0,456