1 2cos x

1 2cos x

Input
2 cos(x)
Alternate form
e^(-i x) + e^(i x)
Roots
x = pi n – pi/2, n element Z
Series expansion at x=0
2 – x^2 + x^4/12 + O(x^6)
(Taylor series)
Derivative
d/dx(2 cos(x)) = -2 sin(x)
Indefinite integral
integral 2 cos(x) dx = 2 sin(x) + constant
Global maxima
max{2 cos(x)} = 2 at x = 2 pi n for integer n
Definite integral
integral_0^(pi/2) 2 cos(x) dx = 2
Definite integral mean square
integral_0^(2 pi) (2 cos^2(x))/pi dx = 2

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