Solve Parametric Equations | Step-by-Step Guide

[cmut]

I have tirelessly tried to solve this out seems i need smnes help: if x=2+7cosθ and y=8+3sinθ show that d²y/dx²=(-3cosec³θ)/49

 

[mfb]

I have tirelessly tried to solve this

You could post what you tried so far.

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.

 

[cmut]

I used the formula for d²y/dx²=(d/dθ dy/dx)/dx/dθ, i further used the quotient rule to simplify the expression and found they are not the same i got 21cosec²θ/49...it seems right but would you think otherwise? i greatly appreciate your feedback Mfb

 

[mfb]

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

 

[HallsofIvy]

I have tirelessly tried to solve this out seems i need smnes help: if x=2+7cosθ and y=8+3sinθ show that d²y/dx²=(-3cosec³θ)/49

dx/dθ= -7 sin(θ) and dy/dθ= 3 cos(θ) so dy/dx= (-3/7) cot(θ)

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)