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## Main Question or Discussion Point

I have tirelessly tried to solve this out seems i need smnes help: if x=2+7cosθ and y=8+3sinθ show that d

^{2}y/dx^{2}=(-3cosec^{3}θ)/49- Thread starter cmut
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I have tirelessly tried to solve this out seems i need smnes help: if x=2+7cosθ and y=8+3sinθ show that d^{2}y/dx^{2}=(-3cosec^{3}θ)/49

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mfb

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You could post what you tried so far.I have tirelessly tried to solve this

You can derive an expression y=f(x). Alternatively, there is a nice way to get an expression f(x,y)=0, which can be derived afterwards.

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mfb

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Okay, I checked it myself, and I get the same result as you.

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HallsofIvy

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dx/dθ= -7 sin(θ) and dy/dθ= 3 cos(θ) so dy/dx= (-3/7) cot(θ)I have tirelessly tried to solve this out seems i need smnes help: if x=2+7cosθ and y=8+3sinθ show that d^{2}y/dx^{2}=(-3cosec^{3}θ)/49

Then d^2y/dx= d/dx(-(3/7) cot(θ))= (3/7) csc^2(θ) dθ/dx= (3/7) csc^2(θ)/(-7 sin(θ))= -(3/49)csc^3(θ)

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