Cos4x
| Input |
|---|
| cos(4 x) |
| Roots |
| x = (pi n)/4 – pi/8, n element Z |
| Series expansion at x=0 |
| 1 – 8 x^2 + (32 x^4)/3 + O(x^6) (Taylor series) |
| Derivative |
| d/dx(cos(4 x)) = -4 sin(4 x) |
| Indefinite integral |
| integral cos(4 x) dx = 1/4 sin(4 x) + constant |
| Global maxima |
| max{cos(4 x)} = 1 at x = (pi n)/2 for integer n |
| Definite integral |
| integral_0^(pi/8) cos(4 x) dx = 1/4 = 0.25 |
| Definite integral mean square |
| integral_0^(pi/2) (2 cos^2(4 x))/pi dx = 1/2 = 0.5 |