# $\cot{(30^°)}$ value

$\cot{(30^°)} \,=\, \sqrt{3}$

The value of cotangent in a thirty degrees right triangle is called the cot of angle thirty degrees.

## Introduction

The co-tangent of angle thirty degrees is a value that represents the ratio of lengths of adjacent side to opposite side when the angle of a right triangle equals to thirty degrees.

According to Sexagesimal system, the cotangent of angle thirty degrees is written as $\cot{(30^°)}$ and its exact value is equal to square root of three, which is an irrational number and it is written mathematically in the following form.

$\cot{(30^°)} \,=\, \sqrt{3}$

The following is the value of cot of thirty degrees in decimal form.

$\cot{(30^°)} \,=\, 1.7320508075\cdots$

$\implies$ $\cot{(30^°)} \,\approx\, 1.7321$

The cot of angle thirty degrees can also be expressed in two other mathematical forms in trigonometry.

### circular system

In mathematics, the cotangent of angle thirty degrees is written as cot of quotient of pi by six radian in circular system and it is written as $\cot{\Big(\dfrac{\pi}{6}\Big)}$ mathematically in trigonometry.

$\cot{\Big(\dfrac{\pi}{6}\Big)} \,=\, \sqrt{3}$

### Centesimal system

The cot thirty degrees is also written as cotangent of angle thirty three and one third grades and it is expressed in mathematical form as $\cot{\Big(33\dfrac{1}{3}^g\Big)}$ in Centesimal system.

$\cot{\Big(33\dfrac{1}{3}^g\Big)} \,=\, \sqrt{3}$

#### Proofs

In mathematics, the exact value of cotangent of thirty degrees can be derived possibly in three distinct mathematical methods.

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