Calculate arccos
| Input |
|---|
| cos^(-1)(x) |
| Root |
| x = 1 |
| Series expansion at x=-1 |
| pi – sqrt(2) sqrt(x + 1) – (x + 1)^(3/2)/(6 sqrt(2)) – (3 (x + 1)^(5/2))/(80 sqrt(2)) – (5 (x + 1)^(7/2))/(448 sqrt(2)) – (35 (x + 1)^(9/2))/(9216 sqrt(2)) + O((x + 1)^5) (Puiseux series) |
| Series expansion at x=0 |
| pi/2 – x – x^3/6 – (3 x^5)/40 + O(x^6) (Taylor series) |
| Series expansion at x=1 |
| (-1)^(ceiling((arg(x – 1))/(2 pi))) (i sqrt(2) sqrt(x – 1) – (i (x – 1)^(3/2))/(6 sqrt(2)) + (3 i (x – 1)^(5/2))/(80 sqrt(2)) – (5 i (x – 1)^(7/2))/(448 sqrt(2)) + (35 i (x – 1)^(9/2))/(9216 sqrt(2)) + O((x – 1)^(11/2))) |
| Series expansion at x=∞ |
| 1/2 i (2 log(x) + log(4)) – i/(4 x^2) – (3 i)/(32 x^4) + O((1/x)^6) (generalized Puiseux series) |
| Derivative |
| d/dx(cos^(-1)(x)) = -1/sqrt(1 – x^2) |
| Indefinite integral |
| integral cos^(-1)(x) dx = x cos^(-1)(x) – sqrt(1 – x^2) + constant |
| Global maximum |
| max{cos^(-1)(x)} = pi at x = -1 |
| Global minimum |
| min{cos^(-1)(x)} = 0 at x = 1 |