[Not Homework] Polar Equation Problem Involved Tangents

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SUMMARY

The discussion revolves around solving a polar equation problem involving tangents, specifically using the integral formula \(\int_{a}^{b} \sqrt { (\frac{dr}{dθ})^2 + r^2 }\, dθ\). Participants highlight the symmetry of the figure, noting that if one point is at (r,θ), the corresponding point is at (r,θ+π/2). This insight aids in understanding the geometric relationships within the problem, facilitating the derivation of the necessary functions for solving the equation.

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  • Understanding of polar coordinates and their representation
  • Familiarity with calculus, specifically integration techniques
  • Knowledge of derivatives and their applications in polar equations
  • Experience with geometric interpretations of mathematical problems
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  • Learn advanced integration techniques for polar coordinates
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Students preparing for exams in calculus, particularly those focusing on polar equations, as well as educators seeking to enhance their teaching methods in this area.

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Not homework, just trying to learn how to solve this problem for an exam.

Homework Statement



https://dl.dropbox.com/u/23889576/Screenshots/10.png

Homework Equations



[itex]\int_{a}^{b} \sqrt { (\frac{dr}{dθ})^2 + r^2 }\, dθ[/itex]

The Attempt at a Solution



Had much difficulty, could not even derive the original derivative function for this problem.
 
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welcome to pf!

hi suporia! welcome to pf! :wink:

the figure is symmetric, so when one bug is at (r,θ), the next is at (r,θ+π/2) …

does that help? :smile:​
 

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