Math Doubts

$\cot{(60^°)}$ value

$\cot{(60^°)} \,=\, \dfrac{1}{\sqrt{3}}$

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

Introduction

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

As per the sexagesimal system, the cotangent of angle sixty degrees is written as $\cot{(60^°)}$ in mathematical form. The exact value for the cot of angle sixty degrees is quotient of one by square root of three. In trigonometric mathematics, it is written in the following mathematical form.

$\cot{(60^°)} \,=\, \dfrac{1}{\sqrt{3}}$

The value of cotangent sixty degrees is an irrational number and its value in decimal form is written as follows.

$\implies$ $\cot{(60^°)} \,=\, 0.5773502691\cdots$

$\implies$ $\cot{(60^°)} \,\approx\, 0.5774$

In mathematics, the cotangent of angle sixty degrees can be written in two other forms.

Circular system

The cotangent of sixty degrees is expressed as the cot of quotient of pi by three radian in circular system. Hence, it is written as $\cot{\Big(\dfrac{\pi}{3}\Big)}$ in mathematical form.

$\cot{\Big(\dfrac{\pi}{3}\Big)} \,=\, \dfrac{1}{\sqrt{3}}$

Centesimal system

According to the centesimal system, the cotangent sixty degrees is expressed as cot of angle sixty six and two third grades. Therefore, it is written as $\cot{\Big(66\frac{2}{3}^{\large g}\Big)}$ in trigonometry.

$\cot{\Big(66\dfrac{2}{3}^g\Big)} \,=\, \dfrac{1}{\sqrt{3}}$

Proofs

In three types of mathematical approaches, the exact value of cotangent of sixty degrees can be proved mathematically.

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