Cos2x 1
| Input |
|---|
| cos(2 x)×1 |
| Result |
| cos(2 x) |
| Roots |
| x = (pi n)/2 – pi/4, n element Z |
| Series expansion at x=0 |
| 1 – 2 x^2 + (2 x^4)/3 + O(x^6) (Taylor series) |
| Derivative |
| d/dx(cos(2 x)×1) = -2 sin(2 x) |
| Indefinite integral |
| integral cos(2 x) dx = sin(x) cos(x) + constant |
| Global maxima |
| max{cos(2 x) 1} = 1 at x = pi n for integer n |
| Definite integral |
| integral_0^(pi/4) cos(2 x) dx = 1/2 = 0.5 |
| Definite integral mean square |
| integral_0^pi (cos^2(2 x))/pi dx = 1/2 = 0.5 |