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Math Help - vector function problem

  1. #1
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    vector function problem

    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.
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  2. #2
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    Your two solutions are: <br />
t = \arcsin \left( {\frac{3}<br />
{4}} \right)\;\& \;t = \pi  - \arcsin \left( {\frac{3}<br />
{4}} \right)
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  3. #3
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    but of course!! thanks a lot!
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  4. #4
    MHF Contributor

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