A5ma4ndrlunawson A5ma4ndrlunawson

19-11-2016
Mathematics

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x = cos(2t) and y = sin(2t)

Find the second derivative

Verified Answer :

nobillionaireNobley nobillionaireNobley

22-11-2016

dy/dx = (dy/dt) / (dx/dt)
dy/dt = 2cos(2t)
dx/dt = -2sin(2t)

dy/dx = 2cos(2t)/-2sin(2t) = -cot(2t)

d^y/dx^2 = d(-1/tan(2t))/dx = (tan(2t) 0 - (-1)2sec^2(2t))/tan^2(2t) = 2sec^2(2t)/tan^2(2t) = 2csc^2 (2t)

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