If x = a (θ – sin θ), y = a (1 + cos θ) find .

Idea of parametric form of differentiation:


If y = f (θ) and x = g(θ) i.e. y is a function of θ and x is also some other function of θ.


Then dy/dθ = f’(θ) and dx/dθ = g’(θ)


We can write :


Given,


x = a (θ – sin θ) ……equation 1


y = a (1+ cos θ) ……equation 2


to find :


As,


So, lets first find dy/dx using parametric form and differentiate it again.


…..equation 3


Similarly,


……equation 4


[


…..equation 5


Differentiating again w.r.t x :



Using product rule and chain rule of differentiation together:



Apply chain rule to determine


[using equation 3]




[ ]



[ 1– cos θ = 2sin2 θ/2]



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