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.
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 |
| $0^\circ$ | $0$ | $0^g$ | $1$ | $1$ | |
| $30^\circ$ | $\dfrac{\pi}{6}$ | $33\dfrac{1}{3}^g$ | $\dfrac{\sqrt{3}}{2}$ | $0.866$ | |
| $45^\circ$ | $\dfrac{\pi}{4}$ | $50^g$ | $\dfrac{1}{\sqrt{2}}$ | $0.7071$ | |
| $60^\circ$ | $\dfrac{\pi}{3}$ | $66\dfrac{2}{3}^g$ | $\dfrac{1}{2}$ | $0.5$ | |
| $90^\circ$ | $\dfrac{\pi}{2}$ | $100^g$ | $0$ | $0$ | |
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 |
| $18^\circ$ | $\dfrac{\pi}{10}$ | $20^g$ | $\dfrac{\sqrt{10+2\sqrt{5}}}{4}$ | $0.9511$ | |
| $36^\circ$ | $\dfrac{\pi}{5}$ | $40^g$ | $\dfrac{\sqrt{5}+1}{4}$ | $0.809$ | |
| $54^\circ$ | $\dfrac{3\pi}{10}$ | $60^g$ | $\dfrac{\sqrt{10-2\sqrt{5}}}{4}$ | $0.5878$ | |