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.

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.

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

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

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.

Latest Math Topics

Latest Math Problems

Email subscription

Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers.
Know more

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.