Thread: 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?

Originally Posted by fardeen_gen

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 (where ) .....

So the solution is found from or .....

So the solution is .

Option D.

Originally Posted by fardeen_gen

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



Means



Or in other words

"Every x that is contained in the set AND "

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



means

"Every x contained with in the set EXCEPT "

Originally Posted by Mathstud28

If you are asking what specifically these intervals represent.

The notation



Means

<< , not

Or in other words

"Every x that is contained in the set AND " << should be OR

Originally Posted by Mathstud28

The notation



means

"Every x contained with in the set EXCEPT "

tsssk

Originally Posted by Moo

huh

You've never seen that? He has it above...

Like

?

That is what I have always seen in Set Theory books.

Originally Posted by Moo

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.

Originally Posted by Mathstud28

You've never seen that? He has it above...

Like

?

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}.

Originally Posted by Mathstud28

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

Originally Posted by Moo

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"