Cos2x 1 2

Cos2x 1 2

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

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