Cos2x-1
| Input |
|---|
| cos(2 x) – 1 |
| Roots |
| x = pi n, n element Z |
| Series expansion at x=0 |
| -2 x^2 + (2 x^4)/3 – (4 x^6)/45 + (2 x^8)/315 + O(x^9) (Taylor series) |
| Derivative |
| d/dx(cos(2 x) – 1) = -2 sin(2 x) |
| Indefinite integral |
| integral (-1 + cos(2 x)) dx = sin(x) cos(x) – x + constant |
| Global maxima |
| max{cos(2 x) – 1} = 0 at x = pi n for integer n |
| Definite integral over a half-period |
| integral_0^(pi/2) (-1 + cos(2 x)) dx = -pi/2~~-1.5708 |
| Definite integral over a period |
| integral_0^pi (-1 + cos(2 x)) dx = -pi~~-3.14159 |
| Definite integral mean square |
| integral_0^pi (-1 + cos(2 x))^2/pi dx = 3/2 = 1.5 |