Math Doubts

Cosine values

Fact-checked:

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.

Table

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
$0^\circ$ $0$ $0^g$ $1$ $1$
Learn more
$30^\circ$ $\dfrac{\pi}{6}$ $33\dfrac{1}{3}^g$ $\dfrac{\sqrt{3}}{2}$ $0.866$
Learn more
$45^\circ$ $\dfrac{\pi}{4}$ $50^g$ $\dfrac{1}{\sqrt{2}}$ $0.7071$
Learn more
$60^\circ$ $\dfrac{\pi}{3}$ $66\dfrac{2}{3}^g$ $\dfrac{1}{2}$ $0.5$
Learn more
$90^\circ$ $\dfrac{\pi}{2}$ $100^g$ $0$ $0$
Learn more

Chart

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
$18^\circ$ $\dfrac{\pi}{10}$ $20^g$ $\dfrac{\sqrt{10+2\sqrt{5}}}{4}$ $0.9511$
Learn more
$36^\circ$ $\dfrac{\pi}{5}$ $40^g$ $\dfrac{\sqrt{5}+1}{4}$ $0.809$
Learn more
$54^\circ$ $\dfrac{3\pi}{10}$ $60^g$ $\dfrac{\sqrt{10-2\sqrt{5}}}{4}$ $0.5878$
Learn more
Ashok Kumar B.E. - Founder of Math Doubts

Ashok Kumar, B.E.

Founder of Math Doubts

A Specialist in Mathematics, Physics, and Engineering with 14 years of experience helping students master complex concepts from basics to advanced levels with clarity and precision.

Story of Math Doubts