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

B
Thread starter Bendelson
Start date Nov 3, 2016
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Cartesian Polar

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The discussion centers on converting the equations y=x^2-1 and y=1-x^2 into polar functions. Participants suggest substituting x and y with polar coordinates, specifically x=r*cos(t) and y=r*sin(t), to derive implicit polar equations. The challenge lies in expressing these equations explicitly in terms of r or t. It is noted that the resulting equations are quadratic in r, and methods such as the quadratic formula or completing the square can be utilized to solve for r. The conversation emphasizes the complexity of the conversion process and the mathematical techniques required.

Nov 3, 2016

Bendelson

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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Nov 4, 2016

lurflurf

Homework Helper

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.

Nov 4, 2016

Bendelson

I was having trouble expressing it explicitly and solving for r or t

Nov 4, 2016

lurflurf

Homework Helper

whate have you tried? It is quadratic in r, either use the quadratic formula or complete the square.

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