Math Doubts

Cosine values

The trigonometric function cosine gives a value for each angle in a right triangle and it is called the cosine value. In trigonometry, there are several cosine values but five cosine values are mostly used and they are also used to derive the remaining cosine function values mathematically.


The special values of cosine function for some standard angles are listed here with mathematical proofs in a tabular form. The following cosine chart is really helpful for learning the advanced trigonometric mathematics.

Angle $(\theta)$ Cosine value $(\cos{\theta})$
Degrees Radian Grades Fraction Decimal Proof
$0^\circ$ $0$ $0^g$ $1$ $1$
$30^\circ$ $\dfrac{\pi}{6}$ $33\dfrac{1}{3}^g$ $\dfrac{\sqrt{3}}{2}$ $0.866$
$45^\circ$ $\dfrac{\pi}{4}$ $50^g$ $\dfrac{1}{\sqrt{2}}$ $0.7071$
$60^\circ$ $\dfrac{\pi}{3}$ $66\dfrac{2}{3}^g$ $\dfrac{1}{2}$ $0.5$
$90^\circ$ $\dfrac{\pi}{2}$ $100^g$ $0$ $0$


The cosine values for different angles are listed in the following tabular form.

Angle $(\theta)$ Cosine value $(\cos{\theta})$
Degrees Radian Grades Fraction Decimal Proof
$18^\circ$ $\dfrac{\pi}{10}$ $20^g$ $\dfrac{\sqrt{10+2\sqrt{5}}}{4}$ $0.9511$
$36^\circ$ $\dfrac{\pi}{5}$ $40^g$ $\dfrac{\sqrt{5}+1}{4}$ $0.809$
Math Doubts

A best free mathematics education website for students, teachers and researchers.

Maths Topics

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Maths Problems

Learn how to solve the maths problems in different methods with understandable steps.

Learn solutions

Subscribe us

You can get the latest updates from us by following to our official page of Math Doubts in one of your favourite social media sites.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved