$\sin{30^\circ}$ value

Exact value

$\sin{30^\circ} \,=\, \dfrac{1}{2}$

Introduction

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

According to sexagesimal system, the angle thirty degrees is written as $30^\circ$ in mathematical form. In trigonometry, the sine of $30$ degrees is written as $\sin{30^\circ}$ and let us learn what the sin $30$ degrees value is.

Fraction form

The exact value of sine of angle $30$ degrees is a rational number and it is equal to $1$ divided by $2$.

$\sin{(30^\circ)}$ $\,=\,$ $\dfrac{1}{2}$

Decimal form

The sin of the standard angle $30$ degrees value is exactly equal to $0.5$ in decimal form.

$\sin{(30^\circ)}$ $\,=\,$ $0.5$

Other forms

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.

$\sin{\Big(33{\large \frac{1}{3}}\Big)} \,=\, \dfrac{1}{2} = 0.5$

Proofs

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.