# Python - Math Module

Some of the most popular mathematical functions are defined in the math module. These include trigonometric functions, representation functions, logarithmic functions, angle conversion functions, etc. In addition, two mathematical constants are also defined in this module.

Pi is a well-known mathematical constant, which is defined as the ratio of the circumference to the diameter of a circle and its value is 3.141592653589793.

Example: Getting Pi Value
``````>>> import math
>>>math.pi
3.141592653589793
``````

Another well-known mathematical constant defined in the math module is e. It is called Euler's number and it is a base of the natural logarithm. Its value is 2.718281828459045.

Example: e Value
``````>>> import math
>>> math.e
2.718281828459045
``````

The math module contains functions for calculating various trigonometric ratios for a given angle. The functions (sin, cos, tan, etc.) need the angle in radians as an argument. We, on the other hand, are used to express the angle in degrees. The math module presents two angle conversion functions: `degrees()` and `radians()`, to convert the angle from degrees to radians and vice versa. For example, the following statements convert the angle of 30 degrees to radians and back (Note: π radians is equivalent to 180 degrees).

Example: Math Radians and Degrees
``````>>> import math
0.5235987755982988
>>> math.degrees(math.pi/6)
29.999999999999996
``````

The following statements show `sin, cos and tan` ratios for the angle of 30 degrees (0.5235987755982988 radians):

Example: sin, cos, tan Calculation
``````>>> import math
>>> math.sin(0.5235987755982988)
0.49999999999999994
>>> math.cos(0.5235987755982988)
0.8660254037844387
>>> math.tan(0.5235987755982988)
0.5773502691896257
``````

You may recall that `sin(30)=0.5`, `cos(30)=32` (which is `0.8660254037844387`) and `tan(30)= 13` (which is 0.`5773502691896257`).

## math.log()

The `math.log()` method returns the natural logarithm of a given number. The natural logarithm is calculated to the base `e`.

Example: log
``````>>> import math
>>>math.log(10)
2.302585092994046
``````

## math.log10()

The `math.log10()` method returns the base-10 logarithm of the given number. It is called the standard logarithm.

Example: log10
``````>>> import math
>>>math.log10(10)
1.0
``````

## math.exp()

The `math.exp()` method returns a float number after raising e to the power of the given number. In other words, `exp(x)` gives `e**x`.

Example: Exponent
``````>>> import math
>>>math.exp(10)
22026.465794806718
``````

This can be verified by the exponent operator.

Example: Exponent Operator **
``````>>> import math
>>>math.e**10
22026.465794806703
``````

## math.pow()

The `math.pow()` method receives two float arguments, raises the first to the second and returns the result. In other words, pow(4,4) is equivalent to 4**4.

Example: Power
``````>>> import math
>>> math.pow(2,4)
16.0
>>> 2**4
16
``````

## math.sqrt()

The `math.sqrt()` method returns the square root of a given number.

Example: Square Root
``````>>> import math
>>> math.sqrt(100)
10.0
>>> math.sqrt(3)
1.7320508075688772
``````

The following two functions are called representation functions. The ceil() function approximates the given number to the smallest integer, greater than or equal to the given floating point number. The `floor()` function returns the largest integer less than or equal to the given number.

Example: Ceil and Floor
``````>>> import math
>>> math.ceil(4.5867)
5
>>> math.floor(4.5687)
4
``````