1/secx

1/secx

Input
1/(sec(x))
Result
cos(x)
Alternate form
e^(-i x)/2 + e^(i x)/2
Roots
x = pi n – pi/2, n element Z
Series expansion at x=0
1 – x^2/2 + x^4/24 + O(x^6)
(Taylor series)
Derivative
d/dx(1/(sec(x))) = -sin(x)
Indefinite integral
integral cos(x) dx = sin(x) + constant
Global maxima
max{1/(sec(x))} = 1 at x = 2 pi n for integer n
Definite integral
integral_0^(pi/2) cos(x) dx = 1
Definite integral mean square
integral_0^(2 pi) (cos^2(x))/(2 pi) dx = 1/2 = 0.5

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