Csc(2x)

Csc(2x)

Input
csc(2 x)
Alternate form assuming x is real
-(2 sin(2 x))/(cos(4 x) – 1)
Roots
(no roots exist)
Series expansion at x=0
1/(2 x) + x/3 + (7 x^3)/45 + (62 x^5)/945 + O(x^6)
(Laurent series)
Derivative
d/dx(csc(2 x)) = -2 cot(2 x) csc(2 x)
Indefinite integral
integral csc(2 x) dx = -1/2 log(cot(x)) + constant
Local maxima
max{csc(2 x)} = -1 at x = pi n – pi/4 for integer n
Local minima
min{csc(2 x)} = 1 at x = pi n + pi/4 for integer n

Leave a Reply

Your email address will not be published. Required fields are marked *