Math Doubts

$\cos{(18^°)}$ value

The value of cosine when the angle of a right triangle equals to $18$ degrees is called the cosine of angle $18$ degrees. In trigonometry, the cosine of angle $18$ degrees expressed as $\cos{(18^°)}$ in mathematical form as per the Sexagesimal system and its exact value in fraction form is written as follows.

$\cos{(18^°)} \,=\, \dfrac{\sqrt{10+2\sqrt{5}}}{4}$

The value of cosine of angle $18$ degrees is an irrational number and it is equal to $0.9510565162\ldots$

$\implies$ $\cos{(18^°)} \,=\, 0.9510565162\ldots$

In decimal form, the approximate value of $\cos{(18^°)}$ is taken as $0.9511$ in trigonometric mathematics.

$\implies$ $\cos{(18^°)} \,\approx\, 0.9511$

Alternative form

The cosine of angle $18$ degrees is written as $\cos{\Big(\dfrac{\pi}{10}\Big)}$ in circular system and also written as $\cos{(20^g)}$ in Centesimal system alternatively.

$(1). \,\,\,$ $\cos{\Big(\dfrac{\pi}{10}\Big)}$ $\,=\,$ $\dfrac{\sqrt{10+2\sqrt{5}}}{4}$ $\,=\,$ $0.9510565162\ldots$

$(2). \,\,\,$ $\cos{(20^g)}$ $\,=\,$ $\dfrac{\sqrt{10+2\sqrt{5}}}{4}$ $\,=\,$ $0.9510565162\ldots$

Proof

Learn how to derive the exact value of the cosine of angle $20$ gradians by the trigonometric and geometric methods.

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