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

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SUMMARY

The discussion focuses on converting the Cartesian equations y=x^2-1 and y=1-x^2 into polar functions. The conversion process involves substituting x and y with their polar equivalents, x=r*cos(t) and y=r*sin(t). Participants noted that the resulting equations yield implicit polar forms, and to derive explicit polar equations, one must solve for r using methods such as the quadratic formula or completing the square. The challenges faced primarily revolve around expressing these equations explicitly in polar coordinates.

PREREQUISITES
  • Understanding of polar coordinates and their relationship to Cartesian coordinates.
  • Familiarity with quadratic equations and methods for solving them.
  • Knowledge of trigonometric functions, specifically sine and cosine.
  • Basic algebra skills for manipulating equations.
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  • Learn how to convert Cartesian equations to polar coordinates in detail.
  • Study the quadratic formula and its applications in solving equations.
  • Explore the concept of implicit vs. explicit equations in mathematics.
  • Investigate examples of polar equations derived from various Cartesian forms.
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Students and educators in mathematics, particularly those studying calculus and coordinate systems, as well as anyone interested in the conversion of equations between Cartesian and polar forms.

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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