- #1

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- 422

## Homework Statement

[itex]y^2 + 3x - x^3 = C, C\in\mathbb{R}\setminus\{0\}[/itex]

## Homework Equations

## The Attempt at a Solution

Keeping in mind that ##\cos ^2\alpha + \sin ^2\alpha = 1##

I would go about it

[tex]\left (\frac{y}{\sqrt{C}}\right )^2 + \left (\frac{\sqrt{3x-x^3}}{\sqrt{C}}\right )^2 = 1 [/tex]

would then?

for some interval for ##t##

##\sin t = \frac{y}{\sqrt{C}}##

##\cos t = \frac{\sqrt{3x-x^3}}{\sqrt{C}}##

this doesn't look so good, can't get anywhere with it

I can't remember this part at all and every piece of parametrization I have been able to google is either for explicit curves or obvious identity parametrizations, in other words, not very helpful.