Math Doubts

$\cos{(60^°)}$ value

$\sin{(60^°)} \,=\, \dfrac{1}{2}$

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

Introduction

The cosine of angle sixty degrees is a value that represents the ratio of lengths of adjacent side to hypotenuse when the angle of a right triangle equals to sixty degrees.

On the basis of the Sexagesimal system, the cosine of angle sixty degrees is written as $\cos{(60^°)}$ in mathematical form. The exact value for the cosine of angle sixty degrees in fraction form is the quotient of one by two. It can be written in the following mathematical form in trigonometry.

$\cos{(60^°)} \,=\, \dfrac{1}{2}$

The value of cosine sixty degrees is a rational number and its value is written in decimal form as follows.

$\implies$ $\cos{(60^°)} \,=\, 0.5$

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

circular system

As per the circular system, the cosine of sixty degrees is expressed as the cosine of quotient of pi by three radian. It is written in mathematical form as $\cos{\Big(\dfrac{\pi}{3}\Big)}$.

$\cos{\Big(\dfrac{\pi}{3}\Big)} \,=\, \dfrac{1}{2}$

Centesimal system

In centesimal system, the cosine sixty degrees is expressed as cosine of angle sixty six and two third grades and it is written in mathematical form as $\cos{\Big(66\frac{2}{3}^{\large g}\Big)}$.

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

Proofs

The exact value of cosine of sixty degrees can be derived in three distinct mathematical methods.

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