Cos2x 1

Cos2x 1

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

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