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Thread: Cylindrical Coordinates

  1. #1
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    Cylindrical Coordinates

    $\displaystyle f(x,y)=\frac{x^2+y^2}{e^{x^2+y^2}}$

    I need to write an equation for this in cylindrical coordinates.

    I know that $\displaystyle r^2=x^2+y^2$ and $\displaystyle x=rcos\theta$
    $\displaystyle y=rsin\theta$

    if I directly substituted I would end up with,

    $\displaystyle \frac{r^2}{e^{r^2}}$

    Am I even close?
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  2. #2
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    Hello, Jesse!

    I'll modify your work slightly . . .


    $\displaystyle f(x,y)\:=\:\frac{x^2+y^2}{e^{x^2+y^2}}$
    Write in cylindrical coordinates.
    We have: . $\displaystyle {\color{blue}z \;=\;\frac{x^2+y^2}{e^{x^2+y^2}}} $

    I know that: .$\displaystyle \begin{array}{ccc}r^2 &=&x^2+y^2 \\ x & = &r\cos\theta \\ y &=&r\sin\theta \\
    {\color{blue}z} &{\color{blue}=}& {\color{blue}z} \end{array}$


    Substituting, I end up with: . $\displaystyle {\color{blue}z} \;=\;\frac{r^2}{e^{r^2}}\qquad{\color{red}\hdots\; \;Right!}$
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