Cosx 3

Cosx 3

Input
cos(x)×3
Result
3 cos(x)
Alternate form
(3 e^(-i x))/2 + (3 e^(i x))/2
Roots
x = pi n – pi/2, n element Z
Series expansion at x=0
3 – (3 x^2)/2 + x^4/8 + O(x^6)
(Taylor series)
Derivative
d/dx(cos(x)×3) = -3 sin(x)
Indefinite integral
integral 3 cos(x) dx = 3 sin(x) + constant
Global maxima
max{cos(x) 3} = 3 at x = 2 pi n for integer n
Definite integral
integral_0^(pi/2) 3 cos(x) dx = 3
Definite integral mean square
integral_0^(2 pi) (9 cos^2(x))/(2 pi) dx = 9/2 = 4.5

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