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Thread: Polar equation to rectangular equation

  1. #1
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    Polar equation to rectangular equation

    Hey, Im having trouble with solving

    r=1-cos2(Θ)


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  2. #2
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    Re: Polar equation to rectangular equation

    First, is that cosine squared rather than 2 times the angle?
    The first would be better written "cos^2(Θ)" and the second "cos(2Θ)". I am going to assume you mean $\displaystyle cos^2(\theta)$.

    So what do you know about converting between Cartesian and polar coordinates?

    Do you, for example, know that $\displaystyle x= r cos(\theta)$ and $\displaystyle y= r sin(\theta)$?
    Do you know that $\displaystyle r= \sqrt{x^2+ y^2}$ and $\displaystyle \theta= arctan\left(\frac{y}{x}\right)$?

    If so you might think about multiplying both sides by $\displaystyle r^2$ so that you have $\displaystyle r^3= r^2- r^2cos^2(\theta)$. That is, then, $\displaystyle (x^2+ y^2)^{3/2}= x^2+ y^2- x^2$ which simplifies to $\displaystyle (x^2+ y^2)^{3/2}= y^2$.
    Last edited by HallsofIvy; Aug 23rd 2018 at 05:32 AM.
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