- #1
cmut
- 2
- 0
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
Solve Parametric Equations | Step-by-Step Guide
- Context: Undergrad
- Thread starter cmut
- Start date
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Discussion Overview
The discussion revolves around solving parametric equations given by x=2+7cosθ and y=8+3sinθ, specifically focusing on finding the second derivative d²y/dx². Participants explore different methods and calculations related to this problem.
Discussion Character
- Technical explanation
- Mathematical reasoning
- Homework-related
Main Points Raised
- One participant expresses difficulty in solving the problem and requests assistance in showing that d²y/dx²=(-3cosec³θ)/49.
- Another participant suggests posting previous attempts and mentions deriving an expression y=f(x) or f(x,y)=0 as possible approaches.
- A participant describes using the formula for d²y/dx² and applying the quotient rule, arriving at a different result of 21cosec²θ/49, and seeks feedback on this outcome.
- One participant confirms that they obtained the same result as the previous poster, indicating a shared calculation.
- A later reply outlines the steps taken to find d²y/dx², including calculating dx/dθ and dy/dθ, and arrives at a result of -(3/49)csc³(θ), which differs from the initial claim.
Areas of Agreement / Disagreement
There is no consensus on the correct value of d²y/dx², as participants have arrived at different results and are discussing their calculations without resolving the discrepancies.
Contextual Notes
Participants' calculations depend on the accuracy of their differentiation steps and the application of the quotient rule, which may not have been fully resolved in the discussion.
- #2
mfb
Mentor
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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.
- #3
cmut
- 2
- 0
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
- #4
mfb
Mentor
- 37,449
- 14,315
Okay, I checked it myself, and I get the same result as you.
- #5
HallsofIvy
Science Advisor
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dx/dθ= -7 sin(θ) and dy/dθ= 3 cos(θ) so dy/dx= (-3/7) cot(θ)cmut said:
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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