Math Doubts

$\cos{(30^°)}$ value

The value of cosine if angle of right triangle equals to $30$ degrees is called cos of angle $30$ degrees. In Sexagesimal angle measuring system, the cosine of angle $30$ degrees is written as $\cos{(30^°)}$.

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

The value of cos of angle $30$ degrees is equal to $\dfrac{\sqrt{3}}{2}$ in fraction form exactly. It is an irrational number and equals to $0.8660254037\ldots$ in decimal form and the same value is considered as $0.866$ approximately in mathematics. The value of cos $30^°$ is usually called as trigonometric ratio or function of standard angle in trigonometry.

Alternative form

Alternatively, the $\cos{(30^°)}$ is mathematically written as $\cos{\Big(\dfrac{\pi}{6}\Big)}$ in circular system and also written as $\cos{\Big({33\dfrac{1}{3}}^g\Big)}$ in centesimal system.

$(1) \,\,\,$ $\cos{\Big(\dfrac{\pi}{6}\Big)}$ $\,=\,$ $\dfrac{\sqrt{3}}{2}$ $\,=\,$ $0.8660254037\ldots$

$(2) \,\,\,$ $\cos{\Big({33\dfrac{1}{3}}^g\Big)}$ $\,=\,$ $\dfrac{\sqrt{3}}{2}$ $\,=\,$ $0.8660254037\ldots$

Proof

You have learnt the exact value of cos of $30$ degrees and it is your turn to know how to derive the $\cos{\Big(\dfrac{\pi}{6}\Big)}$ value in trigonometry.

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