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Thread: vector function problem

  1. #1
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    vector function problem

    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.
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  2. #2
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    Your two solutions are: $\displaystyle
    t = \arcsin \left( {\frac{3}
    {4}} \right)\;\& \;t = \pi - \arcsin \left( {\frac{3}
    {4}} \right)$
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  3. #3
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    but of course!! thanks a lot!
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  4. #4
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    It should also be evident from the symmetry that the other point is (-1.323, 0)
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