Csc(2x)
| Input |
|---|
| csc(2 x) |
| Alternate form assuming x is real |
| -(2 sin(2 x))/(cos(4 x) – 1) |
| Roots |
| (no roots exist) |
| Series expansion at x=0 |
| 1/(2 x) + x/3 + (7 x^3)/45 + (62 x^5)/945 + O(x^6) (Laurent series) |
| Derivative |
| d/dx(csc(2 x)) = -2 cot(2 x) csc(2 x) |
| Indefinite integral |
| integral csc(2 x) dx = -1/2 log(cot(x)) + constant |
| Local maxima |
| max{csc(2 x)} = -1 at x = pi n – pi/4 for integer n |
| Local minima |
| min{csc(2 x)} = 1 at x = pi n + pi/4 for integer n |