Math Doubts

$\cos{(36^°)}$ value

$\cos{(36^°)} \,=\, \dfrac{\sqrt{5}+1}{4}$

The value of cosine in a thirty six degrees right triangle is called the cosine of angle thirty six degrees.

Introduction

The cosine of angle thirty six degrees is a value that represents the ratio of length of adjacent side to length of hypotenuse when the angle of a right triangle is thirty six degrees.

In the sexagesimal system, the cos of angle thirty six degrees is written as $\cos{(36^°)}$ in mathematical form and its exact value in fraction form is the quotient of square root of five plus one by four. It is written in the following mathematical form in trigonometry.

$\cos{(36^°)} \,=\, \dfrac{\sqrt{5}+1}{4}$

The value of cosine of thirty six degrees is an irrational number and its value is written in decimal form as follows.

$\implies$ $\cos{(36^°)} \,=\, 0.8090169943\cdots$

$\implies$ $\cos{(36^°)} \,\approx\, 0.809$

The cos of thirty six degrees is also written in two other forms.

circular system

The cosine of sixty degrees is expressed as the cos of quotient of pi by five radian in the circular system. It is written in mathematical form as $\cos{\Big(\dfrac{\pi}{5}\Big)}$.

$\cos{\Big(\dfrac{\pi}{5}\Big)} \,=\, \dfrac{\sqrt{5}+1}{4}$

Centesimal system

On the basis of centesimal system, the cosine thirty six degrees is written as cosine of angle forty grades and it is written as $\cos{\Big(40^g\Big)}$ in mathematical form.

$\cos{\Big(40^g\Big)} \,=\, \dfrac{\sqrt{5}+1}{4}$

Proofs

Learn how to derive the exact value of cosine of thirty six degrees in trigonometric and geometric methods.

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