# Ruby | Math Module

In Ruby, Modules are defined as a collection of methods, classes, and constants together. Math module consists of the module methods for basic trigonometric and transcendental functions.

#### Module Constants

Name Description
E Define the value of base of natural logrithum e.
PI Define the value of π.

Example:

 `# Ruby code to illustrate the  ` `# Math Module constants ` `puts Math::``E` ` `  `puts Math::``PI`

Output:

```2.718281828459045
3.141592653589793
```

#### Module Methods

1. acos : This method calculate the arc cosine of given value a. It return in the range[0..PI]. The return type of this method is float.
`Math.acos(a)`

Example:

 `# Ruby code to illustrate the  ` `# acos method ` `puts Math.acos(``0``) ` ` `  `# checking its range ` `puts Math.acos(``0``) == Math::``PI``/``2`

Output:

```1.5707963267948966
true
```
2. acosh : This method calculate the inverse hyperbolic cosine of given value a. The return type of this method is float.
`Math.acosh(a)`
3. asin : This method calculate the arc sine of given value a. It return in the range[-PI/2..PI/2]. The return type of this method is float.
`Math.asin(a)`
4. asinh : This method calculate the inverse hyperbolic sine of given value a. The return type of this method is float.
`Math.asinh(a)`

Example:

 `# Ruby code to illustrate the  ` `# asinh method ` `puts Math.asinh(``2``) `

Output:

```1.4436354751788103
```
5. atan : This method calculate the arc of tangent of given of given value a. It returns in the range[-PI..PI]. The return type of this method is the float.
`Math.atan(a)`
6. atanh : This method calculate the inverse hyperbolic tangent of given value a. The return type of this method is float.
`Math.atanh(a)`

Example:

 `# Ruby code to illustrate the  ` `# atanh method ` `puts Math.atanh(``0``.``5``) `

Output:

```0.5493061443340548
```
7. atan2 : This method calculate the arc of tangent of given value a and b. It returns in the range[-PI..PI]. The return type of this method is float.
`Math.atan2(a, b)`
8. cos : This method calculate the cosine of given value a, expressed in radians and return in the range[-1.0..1.0]. The return type of this method is float.
`Math.cos(a)`

Example:

 `# Ruby code to illustrate the  ` `# cos method ` `puts Math.cos(``1``) `

Output:

```0.5403023058681398
```
9. cosh : This method calculate the hyperbolic cosine of given value a and expressed in radians. The return type of this method is float.
`Math.cosh(a)`
10. erf : This method returns the error function of given value a. The return type of this method is float.
`Math.erf(a)`
11. erfc : This method returns the complementary error function of given value a. The return type of this method is float.
`Math.erfc(a)`
12. exp : This method returns the value of ea. The return type of this method is float.
`Math.exp(a)`

Example:

 `# Ruby code to illustrate the  ` `# exp method ` `puts Math.exp(``2``) `

Output:

```7.38905609893065
```
13. frexp : This method returns a two-element array that consisting the normalized fraction and exponent of numeric.
`Math.frexp(numeric)`
14. hypot :This method returns a2+b2. Or in other words it returns the hypotenuse of right-angle triangle with sides a and b. The return type of this method is float.
`Math.hypot(a, b)`

Example:

 `# Ruby code to illustrate the  ` `# hypot method ` `puts Math.hypot(``4``,``5``) `

Output:

```6.4031242374328485
```
15. Idexp : This method returns the value of float * 2 integer. The return type of this method is float.
`Math.Idexp(float, integer)`
16. log : This method returns the natural logarithm of numeric. The return type of this method is float.
`Math.log(numeric)`
17. log10 : This method return the base 10 of the logarithm of numeric. The return type of this method is float.
`Math.log10(numeric)`
18. sin : This method calculate the sine of numeric and expressed in radians. It return in the range[-1.0..1.0 ]. The return type of this method is float.
`Math.sin(numeric)`

Example:

 `# Ruby code to illustrate the  ` `# sin method ` `puts Math.sin(``0``) `

Output:

```0.0
```
19. sinh : This method calculate the hyperbolic sine of numeric and expressed in radians. The return type of this method is float.
`Math.sinh(numeric)`
20. sqrt : This method return the non-negative square root of numeric and raise ArgError if numeric is less than zero. The return type of this method is float.
`Math.sqrt(numeric)`
21. tan : This method return the tangent of numeric and expressed in radians. The return type of this method is float.
`Math.tan(numeric)`
22. tanh : This method calculate the hyperbolic tangent of numeric and expressed in radians. The return type of this method is float.
`Math.tanh(numeric)`

Example:

 `# Ruby code to illustrate the  ` `# tanh method ` `puts Math.tanh(``1``) `

Output:

```0.7615941559557649
```

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