Convert y=x^2-1 & y=1-x^2 to Polar Functions?

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    Cartesian Polar
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Discussion Overview

The discussion revolves around the conversion of the Cartesian equations y=x^2-1 and y=1-x^2 into polar functions. Participants explore the challenges and methods involved in this transformation, focusing on both implicit and explicit forms of the polar equations.

Discussion Character

  • Exploratory, Technical explanation, Mathematical reasoning

Main Points Raised

  • One participant questions whether the equations can be converted to polar functions and expresses difficulties encountered during the process.
  • Another participant suggests substituting x and y with their polar equivalents, proposing that this leads to an implicit polar equation.
  • A different participant indicates challenges in expressing the equations explicitly and solving for r or t.
  • One participant encourages the use of the quadratic formula or completing the square to address the quadratic nature of the equations in r.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the feasibility of converting the equations to polar form, and multiple approaches and challenges are presented without resolution.

Contextual Notes

Participants mention difficulties with explicit expressions and the quadratic nature of the equations, which may depend on specific assumptions or methods for conversion.

Bendelson
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Can y=x^2-1 or y=1-x^2 be converted to polar functions? I was attempting it and kept running into problems. If it's not possible, why not?
 
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Just substitute
x=r*cos(t)
x=r*Sin(t)

This gives an implicit polar equation. If you like, solve for r to get an explicit polar equation.
 
I was having trouble expressing it explicitly and solving for r or t
 
whate have you tried? It is quadratic in r, either use the quadratic formula or complete the square.
 

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