Expressing polar equation as a Cartesian equation

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Homework Statement



Express the following equation in Cartesian form
r = 1 - cos(θ)

Homework Equations


x = r*cos(θ)
y = r*sin(θ)
r^{2} = x^{2} + y^{2}
tan(θ) = \frac{y}{x}

The Attempt at a Solution



I have no idea... a hint would be nice thanks!

BiP
 
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Bipolarity said:

Homework Statement



Express the following equation in Cartesian form
r = 1 - cos(θ)

Homework Equations


x = r*cos(θ)
y = r*sin(θ)
r^{2} = x^{2} + y^{2}
tan(θ) = \frac{y}{x}

The Attempt at a Solution



I have no idea... a hint would be nice thanks!

BiP

If x=r\cos\theta, what is \cos\theta? If x^2+y^2=r^2, and r\geq 0, what is r?
 
gabbagabbahey said:
If x=r\cos\theta, what is \cos\theta? If x^2+y^2=r^2, and r\geq 0, what is r?

Thanks!

BiP
 
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...
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