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posted by  zaika on 11/25/2008 1:33:26 AM  |  status: Closed  

Finding additional polar coordinates.

Course Textbook Chapter Problem
Calculus Calculus: Concepts and Contexts (3rd) by Stewart Appendix H H.1, ex. 1
Question Details:
Hi Everyone,
 
My textbook says that in order to find additional polar coordinates, 'a point represented by (r, θ) can also be represented by (r, θ+2nπ) and (-r, θ+(2n+1)π), where n=any whole number.  I have no problem finding an additional polar coordinate using the first equation, (r, θ+2nπ), but I can never get the coordinates right using the second equation.  To be honest, I don't really understand what 'θ+(2n+1)π' is asking me to do because everytime I plug in n and add the whole thing to θ, I get the wrong answer.  Does anyone know what I'm doing wrong/have any insight? 
 
Thank you in advance for your help.
 

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posted by Bernard on 11/25/2008 8:35:42 AM  |  status: Live
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zaika's comment:
"Thank you! I like positive r's too, but the homework was asking for -r."
Response Details:
You got the first part right: adding a few times 2π does not change the angle, hence
gives the same point.
Another thing you can do is add π to the angle θ and replace r by -r.
If you have the point (1,π/2)  in polar coordinates (the point (0,1) in rectangular coordinates)
we find the point (-1, 3π/2) which is the same point.
And again you may add a few times 2π to the angle: it does not change the point.

However I consider it a bad habit to have negative r's in polar coordinates.
I would recommend to choose your 'r' always positive.
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