vector function problem

**No Logic Sense** · February 28th 2009, 04:41 AM

I have the following vector function:

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

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:

$y(t)=0$
$0=-3+4\cdot \sin t$
$t=0.848$
$x(0.848)=2\cdot \cos (0.848)=1.323$

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

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

**Plato** · February 28th 2009, 05:10 AM

Your two solutions are: $<br /> t = \arcsin \left( {\frac{3}<br /> {4}} \right)\;\& \;t = \pi - \arcsin \left( {\frac{3}<br /> {4}} \right)$

**No Logic Sense** · February 28th 2009, 05:17 AM

but of course!!

thanks a lot!

**HallsofIvy** · February 28th 2009, 05:48 AM

It should also be evident from the symmetry that the other point is (-1.323, 0)

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