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Math Help - value of x when pi/2 < x < pi

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    value of x when pi/2 < x < pi

    find the value of x in the equation 2 sin x - 1 = 0 ,where pi/2 < x < pi

    the choices are: pi/ 6, pi/3, 5pi/6, 2pi/3
    my answer is 2pi/ 3... because it says pi/2 < x < pi because if i translate this to degrees means 90< x < 180. because 2pi/3 is 120 degrees.

    does my answer correct? please check my work Mathhelpforum ... because im really sure with my answer

    thanks
    Last edited by rcs; January 21st 2013 at 06:49 AM.
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    Re: value of x when pi/2 < x < pi

    As you said, in degrees what you have is:

    2sin(x) -1 = 0 where 90< x < 180

    So rearrange for sin(x):

    sin(x) = 1/2

    So find a value of x:

    arcsin(x) = 30 degrees


    Now sketch a graph of sin(x) and look the values of x for your range, where y = 0.5. You should see that x can also be 30 + 360 and 180 - 30 etc.

    Now can you see the value of x for 90< x < 180?
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    Re: value of x when pi/2 < x < pi

    Quote Originally Posted by kinhew93 View Post
    As you said, in degrees what you have is:

    2sin(x) -1 = 0 where 90< x < 180

    So rearrange for sin(x):

    sin(x) = 1/2

    So find a value of x:

    arcsin(x) = 30 degrees


    Now sketch a graph of sin(x) and look the values of x for your range, where y = 0.5. You should see that x can also be 30 + 360 and 180 - 30 etc.

    Now can you see the value of x for 90< x < 180?


    did you mean that my answer is correct? 120 deg. or 2pi/ 3
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    Re: value of x when pi/2 < x < pi

    No your answer is wrong - try putting it back into the equation:

    2sin120 - 1 = sqrt(3) - 1 so the equation isn't satisfied


    What I suggested originally may have been something that you have not yet come across. An alternative approach for this specific question would be sort of what you have already tried - identify the choices that satisfy the restraints and then test them in turn to see if they satisfy the equation. (Of course this is only any good for multiple-choice questions)
    Last edited by kinhew93; January 21st 2013 at 08:44 AM.
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    Re: value of x when pi/2 < x < pi

    Quote Originally Posted by kinhew93 View Post
    No your answer is wrong - try putting it back into the equation:

    2sin120 - 1 = sqrt(3) - 1 so the equation isn't satisfied


    What I suggested originally may have been something that you have not yet come across. An alternative approach for this specific question would be sort of what you have already tried - identify the choices that satisfy the restraints and then test them in turn to see if they satisfy the equation. (Of course this is only any good for multiple-choice questions)

    2sin x - 1 = 0
    2sinx = 1
    Sin x = 1/2
    x = arcsin 1/2
    x = 30
    And so 180 -30 = 150 or pi/6 which satisfies pi/2<x<pi
    is this correct?
    Last edited by rcs; January 21st 2013 at 01:29 PM.
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    Re: value of x when pi/2 < x < pi

    Can we go straight to point what is really the answer among the choices i have given above? Seems like no help i got from here... Too much pointless discussion. My gosh
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    Re: value of x when pi/2 < x < pi

    Quote Originally Posted by rcs View Post
    2sin x - 1 = 0
    2sinx = 1
    Sin x = 1/2
    x = arcsin 1/2
    x = 30
    And so 180 -30 = 150 or pi/6 which satisfies pi/2<x<pi
    is this correct?
    No because 150 degrees = (5pi)/6, which is the answer.

    Can we go straight to point what is really the answer among the choices i have given above? Seems like no help i got from here... Too much pointless discussion. My gosh
    I gave you two clear answers with pretty full working. What's the point in putting an answer if you have no idea what it means? That's just a waste of time.


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