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Math Help - Polar to cartesian

  1. #1
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    Polar to cartesian

    Hi have a question which requires changing polar coordiantes to cartesian for the equation r=exp(titah)

    using
    r = (sqrt(x^2+y^2)
    titah = arctan(y/x)
    r = x/cos(titah) = y/sin(titah)

    i get this equation

    sqrt(x^2+y^2) = exp(arctan(x/y)
    ln(sqrt(x^2+y^2)=arctan(x/y)


    any help on how to separate the variables? to form an equation y=f(x)
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by bcvw85 View Post
    Hi have a question which requires changing polar coordiantes to cartesian for the equation r=exp(titah)

    using
    r = (sqrt(x^2+y^2)
    titah = arctan(y/x)
    r = x/cos(titah) = y/sin(titah)

    i get this equation

    sqrt(x^2+y^2) = exp(arctan(x/y)
    ln(sqrt(x^2+y^2)=arctan(x/y)


    any help on how to separate the variables? to form an equation y=f(x)
    r=e^\theta

    \therefore x^2+y^2=e^{2\arctan\left(\frac{y}{x}\right)}

    \ln(x^2+y^2)=2\arctan\left(\frac{y}{x}\right)

    I don't think we can get y by itself...
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  3. #3
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    Yeah i thought so...was running around in circles in those equations for a while!

    I'm actually trying to find a parameterization(x(t),y(t)) for r=exp(titah).

    So if i can't isolate the y in the equation, how do i perform this parameterization?
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