[Not Homework] Polar Equation Problem Involved Tangents

  • Thread starter Thread starter suporia
  • Start date Start date
  • Tags Tags
    Homework Polar
suporia
Messages
3
Reaction score
0
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



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

The Attempt at a Solution



Had much difficulty, could not even derive the original derivative function for this problem.
 
Last edited by a moderator:
Physics news on Phys.org
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:
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Back
Top