# How to calculate cotangent in python

To calculate the cotangent in Python you can use the trigonometric function **cot()** of the mpmath module.

from mpmath import cot

cot(x)

The parameter x is the angle in radians.

The cot() function returns the cotangent of the angle.

**What is the cotangent? **In trigonometry the cotangent is the ratio between the cosine and the sine. The cotangent tends to infinity at an angle equal to zero. It is nothing in a 90 ° angle.

**Alternative methods**

The cotangent can also be calculated using the inverse of the tangent

from math import tan

print(1/tan(x))

Alternatively, using the ratio of the cosine to the sine.

from math import cos,sin

print(cos(x)/sin(x))

**Examples**

__Example 1__

To calculate the cotangent of an angle of 45 °

from math import radians

from mpmath import cot

x=radians(45)

cot(x)

The radians () function converts the angle measurement from sexagesimal to radians.

The **cot()** function calculates the cotangent.

mpf('1.0')

The cotangent of an angle of 45 ° is equal to 1.

__Example 2__

The same result can be obtained by calculating the inverse of the tangent.

from math import tan

x=radians(45)

print(1/tan(x))

The output is as follows

mpf('1.0000000000000002')

__Example 3__

The cotangent can also be calculated as the ratio between the cosine and sine trigonometric functions of the same angle.

from math import cos,sin

x=radians(45)

print(cos(x)/sin(x))

The output is

1.0

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