Cos3x 1 2
| Input |
|---|
| cos(3 x)×1×2 |
| Result |
| 2 cos(3 x) |
| Roots |
| x = (pi n)/3 – pi/6, n element Z |
| Series expansion at x=0 |
| 2 – 9 x^2 + (27 x^4)/4 + O(x^6) (Taylor series) |
| Derivative |
| d/dx(cos(3 x)×2) = -6 sin(3 x) |
| Indefinite integral |
| integral 2 cos(3 x) dx = 2/3 sin(3 x) + constant |
| Global maxima |
| max{cos(3 x) 2} = 2 at x = (2 pi n)/3 for integer n |
| Definite integral |
| integral_0^(pi/6) 2 cos(3 x) dx = 2/3~~0.666667 |
| Definite integral mean square |
| integral_0^((2 pi)/3) (6 cos^2(3 x))/pi dx = 2 |