Math Doubts

$\sec{(30^°)}$ 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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