I have the following vector function:

$\displaystyle \overrightarrow{r}(t)=\binom{2\cdot \cos t}{-3+4\cdot \sin t} , t\in [0;2\pi]$

I need to find the intersections with the x-axis.

I found the first one (the green cross in the image) by doing the following:

$\displaystyle y(t)=0$

$\displaystyle 0=-3+4\cdot \sin t$

$\displaystyle t=0.848$

$\displaystyle x(0.848)=2\cdot \cos (0.848)=1.323$

So the intersection is $\displaystyle P(1.323;0)$

My question is, how do I find the other intersection? I have tried to subtract with $\displaystyle \pi$ but didn't help.