# Math

A built-in object that has properties and methods for mathematical constants and functions. For example, the Math object's PI property has the value of pi.

#### Created by

The Math object is a top-level, predefined JavaScript object. You can automatically access it without using a constructor or calling a method.

#### Description

All properties and methods of Math are static. You refer to the constant PI as Math.PI and you call the sine function as Math.sin(x), where x is the method's argument. Constants are defined with the full precision of real numbers in JavaScript.

It is often convenient to use the with statement when a section of code uses several Math constants and methods, so you don't have to type "Math" repeatedly. For example,

with (Math) {
a = PI * r*r
y = r*sin(theta)
x = r*cos(theta)
}

#### Method Summary

In addition, this object inherits the watch and unwatch methods from Object.

## abs

Returns the absolute value of a number.

abs(x)

#### Examples

The following function returns the absolute value of the variable x:

function getAbs(x) {
return Math.abs(x)
}

#### Description

Because abs is a static method of Math, you always use it as Math.abs(), rather than as a method of a Math object you created.

## acos

Returns the arccosine (in radians) of a number.

acos(x)

#### Description

The acos method returns a numeric value between 0 and pi radians. If the value of number is outside this range, it returns NaN.

Because acos is a static method of Math, you always use it as Math.acos(), rather than as a method of a Math object you created.

#### Examples

The following function returns the arccosine of the variable x:

function getAcos(x) {
return Math.acos(x)
}
If you pass -1 to getAcos, it returns 3.141592653589793; if you pass 2, it returns NaN because 2 is out of range.

Math.asin, Math.atan, Math.atan2, Math.cos, Math.sin, Math.tan

## asin

Returns the arcsine (in radians) of a number.

asin(x)

#### Description

The asin method returns a numeric value between -pi/2 and pi/2 radians. If the value of number is outside this range, it returns NaN.

Because asin is a static method of Math, you always use it as Math.asin(), rather than as a method of a Math object you created.

#### Examples

The following function returns the arcsine of the variable x:

function getAsin(x) {
return Math.asin(x)
}
If you pass getAsin the value 1, it returns 1.570796326794897 (pi/2); if you pass it the value 2, it returns NaN because 2 is out of range.

Math.acos, Math.atan, Math.atan2, Math.cos, Math.sin, Math.tan

## atan

Returns the arctangent (in radians) of a number.

atan(x)

#### Description

The atan method returns a numeric value between -pi/2 and pi/2 radians.

Because atan is a static method of Math, you always use it as Math.atan(), rather than as a method of a Math object you created.

#### Examples

The following function returns the arctangent of the variable x:

function getAtan(x) {
return Math.atan(x)
}
If you pass getAtan the value 1, it returns 0.7853981633974483; if you pass it the value .5, it returns 0.4636476090008061.

Math.acos, Math.asin, Math.atan2, Math.cos, Math.sin, Math.tan

## atan2

Returns the arctangent of the quotient of its arguments.

atan2(y, x)

#### Description

The atan2 method returns a numeric value between -pi and pi representing the angle theta of an (x,y) point. This is the counterclockwise angle, measured in radians, between the positive X axis, and the point (x,y). Note that the arguments to this function pass the y-coordinate first and the x-coordinate second.

atan2 is passed separate x and y arguments, and atan is passed the ratio of those two arguments.

Because atan2 is a static method of Math, you always use it as Math.atan2(), rather than as a method of a Math object you created.

#### Examples

The following function returns the angle of the polar coordinate:

function getAtan2(x,y) {
return Math.atan2(x,y)
}
If you pass getAtan2 the values (90,15), it returns 1.4056476493802699; if you pass it the values (15,90), it returns 0.16514867741462683.

Math.acos, Math.asin, Math.atan, Math.cos, Math.sin, Math.tan

## ceil

Returns the smallest integer greater than or equal to a number.

ceil(x)

#### Description

Because ceil is a static method of Math, you always use it as Math.ceil(), rather than as a method of a Math object you created.

#### Examples

The following function returns the ceil value of the variable x:

function getCeil(x) {
return Math.ceil(x)
}
If you pass 45.95 to getCeil, it returns 46; if you pass -45.95, it returns -45.

Math.floor

## cos

Returns the cosine of a number.

cos(x)

#### Description

The cos method returns a numeric value between -1 and 1, which represents the cosine of the angle.

Because cos is a static method of Math, you always use it as Math.cos(), rather than as a method of a Math object you created.

#### Examples

The following function returns the cosine of the variable x:

function getCos(x) {
return Math.cos(x)
}
If x equals 2*Math.PI, getCos returns 1; if x equals Math.PI, the getCos method returns -1.

Math.acos, Math.asin, Math.atan, Math.atan2, Math.sin, Math.tan

## E

Euler's constant and the base of natural logarithms, approximately 2.718.

#### Description

Because E is a static property of Math, you always use it as Math.E, rather than as a property of a Math object you created.

#### Examples

The following function returns Euler's constant:

function getEuler() {
return Math.E
}

## exp

Returns Ex, where x is the argument, and E is Euler's constant, the base of the natural logarithms.

exp(x)

#### Description

Because exp is a static method of Math, you always use it as Math.exp(), rather than as a method of a Math object you created.

#### Examples

The following function returns the exponential value of the variable x:

function getExp(x) {
return Math.exp(x)
}
If you pass getExp the value 1, it returns 2.718281828459045.

Math.E, Math.log, Math.pow

## floor

Returns the largest integer less than or equal to a number.

floor(x)

#### Description

Because floor is a static method of Math, you always use it as Math.floor(), rather than as a method of a Math object you created.

#### Examples

The following function returns the floor value of the variable x:

function getFloor(x) {
return Math.floor(x)
}
If you pass 45.95 to getFloor, it returns 45; if you pass -45.95, it returns -46.

Math.ceil

## LN10

The natural logarithm of 10, approximately 2.302.

#### Examples

The following function returns the natural log of 10:

function getNatLog10() {
return Math.LN10
}

#### Description

Because LN10 is a static property of Math, you always use it as Math.LN10, rather than as a property of a Math object you created.

## LN2

The natural logarithm of 2, approximately 0.693.

#### Examples

The following function returns the natural log of 2:

function getNatLog2() {
return Math.LN2
}

#### Description

Because LN2 is a static property of Math, you always use it as Math.LN2, rather than as a property of a Math object you created.

## log

Returns the natural logarithm (base E) of a number.

log(x)

#### Description

If the value of number is negative, the return value is always NaN.

Because log is a static method of Math, you always use it as Math.log(), rather than as a method of a Math object you created.

#### Examples

The following function returns the natural log of the variable x:

function getLog(x) {
return Math.log(x)
}
If you pass getLog the value 10, it returns 2.302585092994046; if you pass it the value 0, it returns -Infinity; if you pass it the value -1, it returns NaN because -1 is out of range.

Math.exp, Math.pow

## LOG10E

The base 10 logarithm of E (approximately 0.434).

#### Examples

The following function returns the base 10 logarithm of E:

function getLog10e() {
return Math.LOG10E
}

#### Description

Because LOG10E is a static property of Math, you always use it as Math.LOG10E, rather than as a property of a Math object you created.

## LOG2E

The base 2 logarithm of E (approximately 1.442).

#### Examples

The following function returns the base 2 logarithm of E:

function getLog2e() {
return Math.LOG2E
}

#### Description

Because LOG2E is a static property of Math, you always use it as Math.LOG2E, rather than as a property of a Math object you created.

## max

Returns the larger of two numbers.

max(x,y)

#### Description

Because max is a static method of Math, you always use it as Math.max(), rather than as a method of a Math object you created.

#### Examples

The following function evaluates the variables x and y:

function getMax(x,y) {
return Math.max(x,y)
}
If you pass getMax the values 10 and 20, it returns 20; if you pass it the values -10 and -20, it returns -10.

Math.min

## min

Returns the smaller of two numbers.

min(x,y)

#### Description

Because min is a static method of Math, you always use it as Math.min(), rather than as a method of a Math object you created.

#### Examples

The following function evaluates the variables x and y:

function getMin(x,y) {
return Math.min(x,y)
}
If you pass getMin the values 10 and 20, it returns 10; if you pass it the values -10 and -20, it returns -20.

Math.max

## PI

The ratio of the circumference of a circle to its diameter, approximately 3.14159.

#### Examples

The following function returns the value of pi:

function getPi() {
return Math.PI
}

#### Description

Because PI is a static property of Math, you always use it as Math.PI, rather than as a property of a Math object you created.

## pow

Returns base to the exponent power, that is, baseexponent.

pow(x,y)

#### Description

Because pow is a static method of Math, you always use it as Math.pow(), rather than as a method of a Math object you created.

#### Examples

function raisePower(x,y) {
return Math.pow(x,y)
}
If x is 7 and y is 2, raisePower returns 49 (7 to the power of 2).

Math.exp, Math.log

## random

Returns a pseudo-random number between 0 and 1. The random number generator is seeded from the current time, as in Java.

random()

None.

#### Description

Because random is a static method of Math, you always use it as Math.random(), rather than as a method of a Math object you created.

#### Examples

//Returns a random number between 0 and 1
function getRandom() {
return Math.random()
}

## round

Returns the value of a number rounded to the nearest integer.

round(x)

#### Description

If the fractional portion of number is .5 or greater, the argument is rounded to the next higher integer. If the fractional portion of number is less than .5, the argument is rounded to the next lower integer.

Because round is a static method of Math, you always use it as Math.round(), rather than as a method of a Math object you created.

#### Examples

//Returns the value 20
x=Math.round(20.49)
//Returns the value 21
x=Math.round(20.5)
//Returns the value -20
x=Math.round(-20.5)
//Returns the value -21
x=Math.round(-20.51)

## sin

Returns the sine of a number.

sin(x)

#### Description

The sin method returns a numeric value between -1 and 1, which represents the sine of the argument.

Because sin is a static method of Math, you always use it as Math.sin(), rather than as a method of a Math object you created.

#### Examples

The following function returns the sine of the variable x:

function getSine(x) {
return Math.sin(x)
}
If you pass getSine the value Math.PI/2, it returns 1.

Math.acos, Math.asin, Math.atan, Math.atan2, Math.cos, Math.tan

## sqrt

Returns the square root of a number.

sqrt(x)

#### Description

If the value of number is negative, sqrt returns NaN.

Because sqrt is a static method of Math, you always use it as Math.sqrt(), rather than as a method of a Math object you created.

#### Examples

The following function returns the square root of the variable x:

function getRoot(x) {
return Math.sqrt(x)
}
If you pass getRoot the value 9, it returns 3; if you pass it the value 2, it returns 1.414213562373095.

## SQRT1_2

The square root of 1/2; equivalently, 1 over the square root of 2, approximately 0.707.

#### Examples

The following function returns 1 over the square root of 2:

function getRoot1_2() {
return Math.SQRT1_2
}

#### Description

Because SQRT1_2 is a static property of Math, you always use it as Math.SQRT1_2, rather than as a property of a Math object you created.

## SQRT2

The square root of 2, approximately 1.414.

#### Examples

The following function returns the square root of 2:

function getRoot2() {
return Math.SQRT2
}

#### Description

Because SQRT2 is a static property of Math, you always use it as Math.SQRT2, rather than as a property of a Math object you created.

## tan

Returns the tangent of a number.

tan(x)

#### Description

The tan method returns a numeric value that represents the tangent of the angle.

Because tan is a static method of Math, you always use it as Math.tan(), rather than as a method of a Math object you created.

#### Examples

The following function returns the tangent of the variable x:

function getTan(x) {
return Math.tan(x)
}