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Math Help - sine inequality

  1. #1
    Super Member fardeen_gen's Avatar
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    sine inequality

    The set of all x in the interval [0, π] for which 2 sin^2 x - 3 sin x + 1 ≥ 0 is?

    I got three values of x:
    π/6, 5π/6 and π/2

    Options for the question are:
    A) [π/6, 5π/6] U {π/2}
    B) [π/6, 5π/6] - {π/2}
    C) [π/6, 5π/6]
    D) None

    What is the correct option? And can someone explain the methodology behing representing the values in an interval or set?
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  2. #2
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    Quote Originally Posted by fardeen_gen View Post
    The set of all x in the interval [0, π] for which 2 sin^2 x - 3 sin x + 1 ≥ 0 is?

    I got three values of x:
    π/6, 5π/6 and π/2

    Options for the question are:
    A) [π/6, 5π/6] U {π/2}
    B) [π/6, 5π/6] - {π/2}
    C) [π/6, 5π/6]
    D) None

    What is the correct option? And can someone explain the methodology behing representing the values in an interval or set?
    Consider 2u^2 - 3u + 1 \geq 0 (where u = \sin x) .....

    So the solution is found from \sin x \leq \frac{1}{2} or \sin x \geq 1 .....

    So the solution is 0 \leq x \leq \frac{\pi}{6} \, \cup \, x = \frac{\pi}{2} \, \cup \, \frac{5 \pi}{6} \leq x \leq \pi.

    Option D.
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by fardeen_gen View Post
    The set of all x in the interval [0, π] for which 2 sin^2 x - 3 sin x + 1 ≥ 0 is?

    I got three values of x:
    π/6, 5π/6 and π/2

    Options for the question are:
    A) [π/6, 5π/6] U {π/2}
    B) [π/6, 5π/6] - {π/2}
    C) [π/6, 5π/6]
    D) None

    What is the correct option? And can someone explain the methodology behing representing the values in an interval or set?
    If you are asking what specifically these intervals represent.

    The notation

    [a,b]\cup[c,d]

    Means

    \forall{x}\in[a,n]\wedge[c,d]

    Or in other words

    "Every x that is contained in the set [a,b] AND [c,d]"

    ------------------
    The notation

    [a,b]-d

    means

    "Every x contained with in the set a,b] EXCEPT d"
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  4. #4
    Moo
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    Quote Originally Posted by Mathstud28 View Post
    If you are asking what specifically these intervals represent.

    The notation

    [a,b]\cup[c,d]

    Means

    \forall{x}\in[a,n] {\color{red}\wedge} [c,d] << {\color{red}\vee}, not {\color{red}\wedge}.

    Or in other words

    "Every x that is contained in the set [a,b] AND [c,d]" << should be OR
    Quote Originally Posted by Mathstud28 View Post
    The notation

    [a,b]-{\color{red}\{}d{\color{red}\}}

    means

    "Every x contained with in the set [a,b] EXCEPT d"
    tsssk
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  5. #5
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Moo View Post
    huh
    You've never seen that? He has it above...

    Like

    A\cup{C}-D?

    That is what I have always seen in Set Theory books.
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  6. #6
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Moo View Post
    tsssk
    My bad...I knew it was or...

    Because it means all the elements of two sets that are included in either. So if an element is included in one set and not the other it is still included in the union of the two sets.
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  7. #7
    Moo
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    Quote Originally Posted by Mathstud28 View Post
    You've never seen that? He has it above...

    Like

    A\cup{C}-D?

    That is what I have always seen in Set Theory books.
    For this notation, yes, but not when dealing with such intervals. d represents a single element, so in general (dunno what your book says.) you have to put it in brackets {d}.

    Quote Originally Posted by Mathstud28 View Post
    My bad...I knew it was or...

    Because it means all the elements of two sets that are included in either. So if an element is included in one set and not the other it is still included in the union of the two sets.
    Of course... you know everything, but you don't take enough care to read yourself............... when someone tells you the solution, it's always "I would have done this way !" "i knew it was that !"

    Tsssk
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  8. #8
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Moo View Post
    For this notation, yes, but not when dealing with such intervals. d represents a single element, so in general (dunno what your book says.) you have to put it in brackets {d}.

    Plus, I edited my post, to correct your blunders.
    Yes, Moo...I like how when I have a typo its a "blunder" but when somone else does it "N'inquiete pas, tout le monde peut se tromper"
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