Cos4x

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

Leave a Reply

Your email address will not be published. Required fields are marked *