Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Sin(x/2) = x/4

  1. Dec 30, 2009 #1
    1. The problem statement, all variables and given/known data
    Solve for x.


    2. Relevant equations
    Given sin(x/2) = x/4.


    3. The attempt at a solution
    no idea. the question gives a hint: use graphical method.
     
  2. jcsd
  3. Dec 30, 2009 #2
    You just have to graph y=sin(x/2) and y=x/4 and find the intersection pts.
     
  4. Dec 30, 2009 #3
    your solution comes as mentioned below

    1. draw a curve of x vs sin(x/2)
    2. draw a second curve of "x vs x/4"

    The solution for x is where both the curves intersect. these are two points

    x=0
    and
    x=3.8

    you can find the resultant chart in attached file.
     

    Attached Files:

  5. Jan 3, 2010 #4
    Plotting [tex]\sin(x/2)[/tex] vs. x and [tex]x/4[/tex] is the way to go indeed.

    You can plot this another way also.
    Rearranging

    [tex]sin(x/2) = x/4[/tex]

    to

    [tex]sin(x/2) - x/4 = 0[/tex]

    and plotting where the curve crosses the x axis is also another way. It crosses three times. At exactly x=0 and at x equals approximately -3.8 and approximately +3.8.
    Close up you see the "zero-crossings" of the x-axis at {-3.8,0,3.8} and if you zoom out you see the curve does not cross at any other points (as far as we can see).
     

    Attached Files:

  6. Jan 3, 2010 #5
    Here it is from very far away.
     

    Attached Files:

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook