The trigonometric function sine gives a value for every angle in a right triangle and it is called the sine value. There are many sine values in trigonometric mathematics but five sine values are mostly used in mathematics and they can be used to derive the remaining sine function values.
The special values of sine function for some standard angles are given here with proofs in a tabular form. The following sine chart is really useful in mathematics for studying the trigonometry in advanced level.
| Angle $(\theta)$ | Sine value $(\sin{\theta})$ | ||||
|---|---|---|---|---|---|
| Degrees | Radian | Grades | Fraction | Decimal | Proof |
| $0^\circ$ | $0$ | $0^g$ | $0$ | $0$ | |
| $30^\circ$ | $\dfrac{\pi}{6}$ | $33\dfrac{1}{3}^g$ | $\dfrac{1}{2}$ | $0.5$ | |
| $45^\circ$ | $\dfrac{\pi}{4}$ | $50^g$ | $\dfrac{1}{\sqrt{2}}$ | $0.7071$ | |
| $60^\circ$ | $\dfrac{\pi}{3}$ | $66\dfrac{2}{3}^g$ | $\dfrac{\sqrt{3}}{2}$ | $0.866$ | |
| $90^\circ$ | $\dfrac{\pi}{2}$ | $100^g$ | $1$ | $1$ | |
The sine values for different angles are listed in the following tabular form.
| Angle $(\theta)$ | Sine value $(\sin{\theta})$ | ||||
|---|---|---|---|---|---|
| Degrees | Radian | Grades | Fraction | Decimal | Proof |
| $15^\circ$ | $\dfrac{\pi}{12}$ | $16\small\dfrac{2}{3}^{\normalsize g\,}$ | $\dfrac{\sqrt{3}-1}{2\sqrt{2}}$ | $0.2588$ | |
| $18^\circ$ | $\dfrac{\pi}{10}$ | $20^g$ | $\dfrac{\sqrt{5}-1}{4}$ | $0.309$ | |
| $36^\circ$ | $\dfrac{\pi}{5}$ | $40^g$ | $\dfrac{\sqrt{10-2\sqrt{5}}}{4}$ | $0.5878$ | |
| $54^\circ$ | $\dfrac{3\pi}{10}$ | $60^g$ | $\dfrac{\sqrt{5}+1}{4}$ | $0.809$ | |
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