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Math Help - Conditional Trigonometric Equations, Helpo!!

  1. #1
    nee
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    Conditional Trigonometric Equations, Helpo!!

    Solve the equation for exact solutions over the interval 0,2

    tan(squared)x + 3 = 0

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    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by nee View Post
    Solve the equation for exact solutions over the interval 0,2

    tan(squared)x + 3 = 0
    \tan^2x+3=0

    There is no such x value that causes this statement to be true.

    Maybe you mean \tan^2x{\color{red}-}3=0??

    --Chris
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    Quote Originally Posted by nee View Post
    Solve the equation for exact solutions over the interval 0,2

    tan(squared)x - 3 = 0
    The one you gave doesn't exist so I'm assuming you made a typo.

    Add 3, then take the square root of both sides. Look on the unit circle to see which angles correspond to  tan = \sqrt{3} over the interval [0,2\pi), which is pretty much the entire unit circle. Those points will be your solutions.
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  4. #4
    nee
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    That's the question as it's written in the text, and the answer given is 0 with a diagonal line through it, whatever that means.
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    Moo
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    Quote Originally Posted by nee View Post
    That's the question as it's written in the text, and the answer given is 0 with a diagonal line through it, whatever that means.
    LoL

    \emptyset. This means that there is no solution. More precisely \{\emptyset\} stands for "the set of the solutions is empty"
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  6. #6
    nee
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    Oh ok. So what kind of work I'm supposed to show to demonstrate how I came to that conclusion?
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    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by nee View Post
    Oh ok. So what kind of work I'm supposed to show to demonstrate how I came to that conclusion?
    Note that you can't have \tan\vartheta=\pm\sqrt{3}i

    Since the tangent would be complex, there wouldn't be a possible solution for x. So our answer would just be an empty set, \left\{\emptyset\right\}
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  8. #8
    nee
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    Why can't you have ? When I punch it into my calculator I get a number.
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    Quote Originally Posted by nee View Post
    Why can't you have ? When I punch it into my calculator I get a number.
    An imaginary number isn't on the x-axis. In order for that number to be a solution to the equation, the equation must intersect the x-axis at that point. Since that point doesn't exist on the x-axis when y = 0, then it is not a solution of the equation.
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  10. #10
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by nee View Post
    Why can't you have ? When I punch it into my calculator I get a number.
    Maybe I should have said this: You will not find an appropriate value for \vartheta that falls in the domain 0\leq\vartheta\leq 2\pi. By the way, my calculator tells me that \vartheta=\pm\frac{\pi}{2}\mp\frac{\ln(2-\sqrt{3})}{2}i which apparently seems like it won't fall in the interval 0\leq\vartheta\leq 2\pi.

    --Chris
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    nee
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    Thanks!
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  12. #12
    nee
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    Thanks!

    nee
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    Super Member flyingsquirrel's Avatar
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    Hi,
    Quote Originally Posted by Moo View Post
    More precisely \{\emptyset\} stands for "the set of the solutions is empty"
    Quote Originally Posted by Chris L T521 View Post
    So our answer would just be an empty set, \left\{\emptyset\right\}
    \{\emptyset\} is the set whose only member is the set \emptyset. Saying that the set of the solutions of \tan^2x+3=0 is \{\emptyset\} means that for x = \emptyset the equation is satisfied. In other words, \tan^2\emptyset +3=0 . I guess we agree that this doesn't make sense at all. To say that the set of the solutions is empty, simply get rid of the two braces : the set of the solutions of \tan^2x+3=0 is \emptyset.
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