# Solving sin2x= (1/2)x

• Sep 13th 2011, 11:08 PM
Effrego
Solving sin2x= (1/2)x
Solving sin2x= (1/2)x (for positive values of x)
I got this as a part of my tutor homework, yet I can't seem to figure it out. It also says to use a graphical method to solve for this equation. I have draw out the lines, but don't know how to find that x intercept point of the 2 lines.
I am also confused to as whether this has anything to do with converting any values to radians as that is part of the current topic, any help would be great, Thanks.
• Sep 14th 2011, 12:07 AM
Sudharaka
Re: Solving sin2x= (1/2)x
Quote:

Originally Posted by Effrego
Solving sin2x= (1/2)x (for positive values of x)
I got this as a part of my tutor homework, yet I can't seem to figure it out. It also says to use a graphical method to solve for this equation. I have draw out the lines, but don't know how to find that x intercept point of the 2 lines.
I am also confused to as whether this has anything to do with converting any values to radians as that is part of the current topic, any help would be great, Thanks.

Hi Effrego,

Draw the two graphs y=sin2x and y=x/2 on a graph paper (only for positive x) and find the point of intersection of the two graphs. x should be taken in radians because otherwise the dimensions of the right and left sides will not match with each other (sin2x is always dimensionless).
• Sep 14th 2011, 05:33 AM
piscoau
Re: Solving sin2x= (1/2)x
Maybe Newton's method may get help(Wink)
by using Newton's method, the solution is 1.237288394.....
This is the only solution for positive number
• Sep 14th 2011, 11:27 PM
CaptainBlack
Re: Solving sin2x= (1/2)x
Quote:

Originally Posted by Sudharaka
...

x should be taken in radians because otherwise the dimensions of the right and left sides will not match with each other (sin2x is always dimensionless).

Units have nothing to do with this both degrees and radians are dimensionless in the required sense.

Use of radians is conventional in most area of mathematics which is why you should use them here unless otherwise instructed, but the same problem could in principle arise in radians, degrees and gradians

CB
• Sep 15th 2011, 12:48 AM
Sudharaka
Re: Solving sin2x= (1/2)x
Quote:

Originally Posted by CaptainBlack
Units have nothing to do with this both degrees and radians are dimensionless in the required sense.

Use of radians is conventional in most area of mathematics which is why you should use them here unless otherwise instructed, but the same problem could in principle arise in radians, degrees and gradians

CB

Yes my mistake, and thanks for pointing it out.
• Sep 15th 2011, 03:42 AM
sbhatnagar
Re: Solving sin2x= (1/2)x
You cannot solve sin(2x)=(1/2)x by algebraic method. The only method to solve this is to graph it or solve it using trial and error method.
The value for x = 0, 1.23729 as calculated by Wolfram Mathematica 7
• Sep 15th 2011, 03:44 AM
HallsofIvy
Re: Solving sin2x= (1/2)x
Quote:

Originally Posted by Effrego
Solving sin2x= (1/2)x (for positive values of x)
I got this as a part of my tutor homework, yet I can't seem to figure it out. It also says to use a graphical method to solve for this equation. I have draw out the lines, but don't know how to find that x intercept point of the 2 lines.
I am also confused to as whether this has anything to do with converting any values to radians as that is part of the current topic, any help would be great, Thanks.

If you use a graphing calculator, you can "zoom" in on the point of intersection and read off the x coordinate. (I assume you are not looking for the obvious solution x= 0.) As Sudharaka said, be sure your calculator is in radian mode.
• Sep 15th 2011, 05:10 AM
CaptainBlack
Re: Solving sin2x= (1/2)x
Quote:

Originally Posted by Effrego
Solving sin2x= (1/2)x (for positive values of x)
I got this as a part of my tutor homework, yet I can't seem to figure it out. It also says to use a graphical method to solve for this equation. I have draw out the lines, but don't know how to find that x intercept point of the 2 lines.
I am also confused to as whether this has anything to do with converting any values to radians as that is part of the current topic, any help would be great, Thanks.

You might want to consider using brackets to make your problem unambiguius. Possible meanings from your equation given the poor notation often seen on the internet are:

$[\sin(x)]^2=\frac{x}{2}$

$\sin(2x)=\frac{x}{2}$

and the less likely:

$\sin(\sin(x))=\frac{x}{2}$

All posters so far have assumed you mean sin(2x)=(x/2)

CB
• Sep 21st 2011, 04:01 AM
Effrego
Re: Solving sin2x= (1/2)x
Well in the end, I asked and saw the homework answers and in there was just the graph sin2x and y=x/2 drawn out, with an line draw from the intersection of those 2 lines to the x axis, and it was just estimated..
• Sep 21st 2011, 05:31 AM
CaptainBlack
Re: Solving sin2x= (1/2)x
Quote:

Originally Posted by Effrego
Well in the end, I asked and saw the homework answers and in there was just the graph sin2x and y=x/2 drawn out, with an line draw from the intersection of those 2 lines to the x axis, and it was just estimated..

Which is what the first post (and a number of others also suggested) in this thread told you to do, did you?

CB