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What the plot would look like

I have attached the question.

**I only need help in the last part of the question.**

I have managed to derive that;

$\displaystyle f(rcos(\theta),rsin(\theta))=\frac{(rcos(\theta))^ 3(rsin(\theta))}{r^6cos^6(\theta)+r^2sin^2(\theta) }=\frac{r^2cos^3(\theta)sin(\theta)}{r^4cos^6( \theta)+sin^2(\theta)}$

However I'm not sure about what this tells me about the plot of the graph nor am I sure of what to do next.

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Re: What the plot would look like

I'd just say that it oscillates between two fixed values, like a normal trigonometric function, since the bottom can't be 0. Differentiate the funtion if need be to find it's maximum and minimum values. Beyond that, the only thing i can recommend is using a computer. See attached pic.

Attachment 23883