$\csc{(30^°)}$ value

$\csc{(30^°)} \,=\, 2$

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

Introduction

The cosecant of angle thirty degrees is a value that represents the ratio of lengths of hypotenuse to opposite side when the angle of a right triangle equals to thirty degrees.

The cosecant of angle thirty degrees in Sexagesimal system is written as $\csc{(30^°)}$ or $\operatorname{cosec}{(30^°)}$. The exact value of cosecant of thirty degrees is equal to two. It is an integer and written in the following mathematical form.

$\csc{(30^°)} \,=\, 2$

The co-secant of angle thirty degrees can be written in two other forms too in trigonometry.

circular system

The cosecant of angle thirty degrees in circular system is written as the cosecant of quotient of pi by six radian. So, it is mathematically written as $\csc{\Big(\dfrac{\pi}{6}\Big)}$ in trigonometric mathematics.

$\csc{\Big(\dfrac{\pi}{6}\Big)} \,=\, 2$

Centesimal system

The cosecant thirty degrees is also written in Centesimal system as the cosecant of angle thirty three and one third grades. It is written as $\csc{\Big(33\dfrac{1}{3}^g\Big)}$ in mathematical form.

$\csc{\Big(33\dfrac{1}{3}^g\Big)} \,=\, 2$

Proofs

The exact value of cosecant of thirty degrees can be proved in three possible methods in mathematics.