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.

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

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


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.

Math Questions

The math problems with solutions to learn how to solve a problem.

Learn solutions

Math Worksheets

The math worksheets with answers for your practice with examples.

Practice now

Math Videos

The math videos tutorials with visual graphics to learn every concept.

Watch now

Subscribe us

Get the latest math updates from the Math Doubts by subscribing us.

Learn more

Math Doubts

A free math education service for students to learn every math concept easily, for teachers to teach mathematics understandably and for mathematicians to share their maths researching projects.

Copyright © 2012 - 2023 Math Doubts, All Rights Reserved