Math Doubts

$\tan{(18°)}$ value

$\tan{(18^°)} \,=\, \dfrac{\sqrt{5}-1}{\sqrt{10+2\sqrt{5}}}$

The value of tangent function when the angle is eighteen degrees in a right triangle, is called the tan of angle eighteen degrees.

Introduction

According to the Sexagesimal system, the tan of eighteen degrees is written in mathematical form as $\tan{(18^°)}$.

Fraction form

The exact value of tangent of angle eighteen degrees can be written in the following fraction form.

$\tan{(18^°)} \,=\, \dfrac{\sqrt{5}-1}{\sqrt{10+2\sqrt{5}}}$

Decimal form

The value of tan of eighteen degrees is an irrational number and the following is the exact value of tan of $18$ degrees in decimal form.

$\tan{(18^°)} \,=\, 0.3249196962\ldots$

The irrational value of tan of eighteen degrees is considered as $0.3249$ approximately in mathematics.

$\implies$ $\tan{(18^°)} \,\approx\, 0.3249$

Other forms

The $\tan{(18^°)}$ is written as $\tan{\Big(\dfrac{\pi}{10}\Big)}$ as per circular system, and also written as $\tan{(20^g)}$ as per Centesimal system.

$(1) \,\,\,$ $\tan{\Big(\dfrac{\pi}{10}\Big)}$ $\,=\,$ $\dfrac{\sqrt{5}-1}{\sqrt{10+2\sqrt{5}}}$ $\,=\,$ $0.3249196962\ldots$

$(2) \,\,\,$ $\tan{(20^g)}$ $\,=\,$ $\dfrac{\sqrt{5}-1}{\sqrt{10+2\sqrt{5}}}$ $\,=\,$ $0.3249196962\ldots$

Proofs

The value of tan of eighteen degrees can be derived in mathematics in two different methods.

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