Given the ellipse $\{(x,y):4x^{2}+9y^{2}=36\}$, find a trajectory $\sigma(t)$ which represent it.

So far, I have this:

The standard equation for an ellipse is:

$\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$

So,

$4x^{2}+9y^{2}=36\}$

$=\left \langle \text{Arithmetic: Divide by}\ 36 \right \rangle$

$\frac{4x^{2}}{36}+\frac{9y^{2}}{36}=\frac{36}{36}$

$=\left \langle \text{Arithmetic} \right \rangle$

$\frac{x^{2}}{9}+\frac{y^{2}}{4}=1$

I don't know how to continue developing the solution, but I think the trajectory could be represented as $(a\cos(t),b\sin(t))$

Some ideas, suggestions to solve this?