# $\sin{(30^°)}$

## Value

$\sin{30^°}$ $\,=\,$ $\dfrac{1}{2}$

### Introduction

When angle of a right triangle is $30^°$, the value of ratio of lengths of opposite side (perpendicular) to hypotenuse is called sine of $30$ degrees and it is simply called as sin $30$ degrees.

#### Sexagesimal System

Sine of angle $30$ degrees is written as $\sin{30^°}$ mathematically in sexagesimal system.

The exact value of sin $30$ degrees in fraction is equal to $\dfrac{1}{2}$.

$\sin{30^{°}} \,=\, \dfrac{1}{2}$

The exact value of sine $30$ degrees in decimal equals to $0.5$.

$\sin{30^{°}} \,=\, 0.5$

#### Circular system

It is written as $\sin{\Big(\dfrac{\pi}{6}\Big)}$ in circular system.

$\sin{\Big(\dfrac{\pi}{6}\Big)} \,=\, \dfrac{1}{2} = 0.5$

#### Centesimal System

It is written as $\sin{\Big(33\dfrac{1}{3}\Big)}$ in centesimal system.

$\sin{\Big(\dfrac{\pi}{6}\Big)} \,=\, \dfrac{1}{2} = 0.5$

### Proof

The value of $\sin{\Big(\dfrac{\pi}{6}\Big)}$ can be derived in trigonometry by geometrical approach. It can be derived possibly in two geometrical methods.

#### Theoretical Approach

Learn how to derive the value of sin of angle $30$ degrees in theoretical geometric method by considering a special relation between lengths of opposite side and hypotenuse when angle of right triangle is $30^°$.

#### Practical Approach

Learn how to derive the value of sine $30$ degrees in geometrical approach experimentally by constructing a right triangle with an angle of $30$ degrees.