The trigonometric function tangent gives a value for each angle in a right triangle and it is called the tangent value. In trigonometric mathematics, there are numerous tan values but five of them are used mostly and they are actually used to derive the remaining tan function values mathematically.
The special values of tangent function for some standard angles are listed here in a tabular form with proofs. The tan chart is really useful to us in studying the advanced trigonometry.
| Angle $(\theta)$ | Tan value $(\tan{\theta})$ | ||||
|---|---|---|---|---|---|
| Degrees | Radian | Grades | Fraction | Decimal | Proof |
| $0^°$ | $0$ | $0^g$ | $0$ | $0$ | |
| $30^°$ | $\dfrac{\pi}{6}$ | $33\dfrac{1}{3}^g$ | $\dfrac{1}{\sqrt{3}}$ | $0.5774$ | |
| $45^°$ | $\dfrac{\pi}{4}$ | $50^g$ | $1$ | $1$ | |
| $60^°$ | $\dfrac{\pi}{3}$ | $66\dfrac{2}{3}^g$ | $\sqrt{3}$ | $1.7321$ | |
| $90^°$ | $\dfrac{\pi}{2}$ | $100^g$ | $\infty$ | $\infty$ | |
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