Cosecant values
The trigonometric function cosecant gives a value for any angle of a right triangle and each value is called the cosecant value. There are numerous cosecant values but five of them are used in most of the cases in trigonometry and they are used to derive the remaining cosecant function values mathematically.
Table
The special values of cosecant function for some standard angles are listed here with proofs in a tabular form. The cosecant chart is really helpful in mathematics for studying the trigonometry in advanced level..
| Angle $(\theta)$ | Cosecant value $(\csc{\theta})$ | ||||
|---|---|---|---|---|---|
| Degrees | Radian | Grades | Fraction | Decimal | Proof |
| $0^°$ | $0$ | $0^g$ | $\infty$ | $\infty$ | |
| $30^°$ | $\dfrac{\pi}{6}$ | $33\dfrac{1}{3}^g$ | $2$ | $2$ | |
| $45^°$ | $\dfrac{\pi}{4}$ | $50^g$ | $\sqrt{2}$ | $1.4142$ | |
| $60^°$ | $\dfrac{\pi}{3}$ | $66\dfrac{2}{3}^g$ | $\dfrac{2}{\sqrt{3}}$ | $1.1547$ | |
| $90^°$ | $\dfrac{\pi}{2}$ | $100^g$ | $1$ | $1$ | |