# $\sec{(30^°)}$ value

$\sec{(30^°)} \,=\, \dfrac{2}{\sqrt{3}}$

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

## Introduction

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

In Sexagesimal system, the secant of angle thirty degrees is written as $\sec{(30^°)}$. Its exact value is equal to quotient of two by square root of three. It is an irrational number and written in the following mathematical form.

$\sec{(30^°)} \,=\, \dfrac{2}{\sqrt{3}}$

The following is the value of secant of thirty degrees in decimal form.

$\sec{(30^°)} \,=\, 1.1547005383\cdots$

$\implies$ $\sec{(30^°)} \,\approx\, 1.1547$

The secant of angle thirty degrees can also be written in two other forms in trigonometric mathematics.

### circular system

The secant of angle thirty degrees is written as the secant of quotient of pi by six radian in circular system. It is mathematically written as $\sec{\Big(\dfrac{\pi}{6}\Big)}$ in mathematics.

$\sec{\Big(\dfrac{\pi}{6}\Big)} \,=\, \dfrac{2}{\sqrt{3}}$

### Centesimal system

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

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

#### Proofs

The exact value of secant of thirty degrees can be derived possibly in three mathematical approaches in mathematics.

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