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I was wondering how can one draw a graph (at least schematic) from given parametric equation, For example I took $$x=a\cos^3(t)\qquad \text{and}\qquad y=a\sin^3(t).$$ Initially I tried to find solution of $x=y$.

And then where it get zero, but I was unable to plot it.

How shall I do it?

Tianlalu
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pde
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  • Do you mean, draw by hand? I would say that the most intuitive approach is to choose values for $t$, plug them into the two equations and then add the created point to the graph. – Matti P. Nov 02 '18 at 06:43
  • In this case you can try to solve for $t$ in the equation for $x$; and then plug in the result for the equation of $y$. – Matti P. Nov 02 '18 at 06:45
  • Yes, but when you plug it in this case you can do, but if equations were different like. X=|cos(4t)|cos(t) and y=|cos(4t)| sin(t) then how to. – pde Nov 02 '18 at 06:50

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Note that $x^{2/3}+y^{2/3}=a^{2/3}$. I've used the Pythagorean identity $\cos^2 t+\sin^2 t=1$ to get rid of $t$. The curve is called an astroid. You can find more information here.

Ernie060
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Andrei
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