Cos3x 1 2

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

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