# $\sin{(60^°)}$ value

$\sin{(60^°)} \,=\, \dfrac{\sqrt{3}}{2}$

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

## Introduction

The sine of angle sixty degrees is a value that represents the ratio of lengths of opposite side to hypotenuse when the angle of a right triangle is equal to sixty degrees.

According to the Sexagesimal system, the sine of angle sixty degrees is written as $\sin{(60^°)}$ in mathematical form. The exact value of sine of angle sixty degrees in fraction form is the quotient of square root of three by two, and it is written in below mathematical form in trigonometry.

$\sin{(60^°)} \,=\, \dfrac{\sqrt{3}}{2}$

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

$\implies$ $\sin{(60^°)} \,=\, 0.8660254037\cdots$

$\implies$ $\sin{(60^°)} \,\approx\, 0.866$

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

### circular system

According to the circular system, the sine of sixty degrees is expressed as the sine of quotient of pi by three radian and it is written in mathematical form as $\sin{\Big(\dfrac{\pi}{3}\Big)}$.

$\sin{\Big(\dfrac{\pi}{3}\Big)} \,=\, \dfrac{\sqrt{3}}{2}$

### Centesimal system

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

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

#### Proofs

The value of sine of sixty degrees can be derived exactly in in three possible different methods in mathematics.

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