1 sinx

1 sinx

Input
1 sin(x)
Result
sin(x)
Alternate form
1/2 i e^(-i x) – 1/2 i e^(i x)
Roots
x = pi n, n element Z
Series expansion at x=0
x – x^3/6 + x^5/120 + O(x^6)
(Taylor series)
Derivative
d/dx(1 sin(x)) = cos(x)
Indefinite integral
integral sin(x) dx = -cos(x) + constant
Global maxima
max{1 sin(x)} = 1 at x = 2 pi n + pi/2 for integer n
Definite integral over a half-period
integral_0^pi sin(x) dx = 2
Definite integral mean square
integral_0^(2 pi) (sin^2(x))/(2 pi) dx = 1/2 = 0.5

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