# value of x when pi/2 < x < pi

• Jan 21st 2013, 05:21 AM
rcs
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 (Crying)

thanks
• Jan 21st 2013, 08:43 AM
kinhew93
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?
• Jan 21st 2013, 09:01 AM
rcs
Re: value of x when pi/2 < x < pi
Quote:

Originally Posted by kinhew93
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
• Jan 21st 2013, 09:38 AM
kinhew93
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)
• Jan 21st 2013, 01:59 PM
rcs
Re: value of x when pi/2 < x < pi
Quote:

Originally Posted by kinhew93
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?
• Jan 21st 2013, 02:02 PM
rcs
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
• Jan 22nd 2013, 07:11 AM
kinhew93
Re: value of x when pi/2 < x < pi
Quote:

Originally Posted by rcs
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.

Quote:

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.

Quote:

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