pi radians.
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y' = (sec(x))^2
Yes, that is a shifted tanX graph, just as you would shift any graft.
y=sinx y=cosxsinx=cosx=>sinx/cosx=1=>tanx=1=>x=45oie.. y=sin45=cos45y=1/(square root of 2)
(tanx+cotx)/tanx=(tanx/tanx) + (cotx/tanx) = 1 + (cosx/sinx)/(sinx/cosx)=1 + cos2x/sin2x = 1+cot2x= csc2x This is a pythagorean identity.
The same as the period of y = sin x. This period is equal to (2 x pi).