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Homework Help: Y= l sin x l < absolute value of sinx

  1. Sep 19, 2010 #1
    1. The problem statement, all variables and given/known data
    y= l sin x l < absolute value of sinx



    2. Relevant equations



    3. The attempt at a solution
    y= l sin x l= sinx, if x>0
    -sinx, if x< 0
    0, if x=0
    I get that part, but when i draw the graph I don't get it
     
  2. jcsd
  3. Sep 19, 2010 #2

    Mark44

    Staff: Mentor

    What about the graph don't you get?
     
  4. Sep 19, 2010 #3
    why are all y values above the x axis?
     
  5. Sep 19, 2010 #4

    eumyang

    User Avatar
    Homework Helper

    Because it's an absolute value. You say that y = | sin x |, so the y-values can only be 0 or positive. If you take the graph of f(x) = sin x (without the absolute value), reflect all of the graph that is below the x-axis, across the x-axis, you will get the graph of y = | sin x |.
     
  6. Sep 19, 2010 #5

    Mark44

    Staff: Mentor

    That's what the absolute value does.

    BTW, what you have here is incorrect -
    It should be
    |sin x| = sin x, if sin x >= 0
    -sin x, if sin x < 0
     
  7. Sep 19, 2010 #6
    ye, i noticed so all y values must be positive? but if i make it into a piecewise function then for sinx, if sinx >=0 then if i input 3pi/2 i would get a negative y value (-1)
     
  8. Sep 19, 2010 #7

    Mark44

    Staff: Mentor

    Actually, the y values for y = |sin x| are nonnegative.

    It's not clear to me what you're asking. |sin (3pi/2)| = |-1| = 1.
     
  9. Sep 19, 2010 #8
    y=sinx if sinx>=0 so if i input a value of 3pi/2, wouldn't that give me a negative number?
     
  10. Sep 19, 2010 #9

    Mark44

    Staff: Mentor

    Yes, but so what? You are working with y = |sin x|.

    The graph of y = |sin x| will agree exactly with the graph of y = sin x wherever sin x is >= 0. For the intervals where y = sin x < 0, the absolute value will flip them across the x-axis.
     
  11. Sep 19, 2010 #10
    k got it, so when x<0 it gets reflected across the x axis, for the other values since we are dealing with absolute value, an aboslute value of a negative is positive. Thanks, only reason I got confused is when you put it in from sinx, if sinx>=0 and when sinx<0 thanks
     
  12. Sep 20, 2010 #11

    Mark44

    Staff: Mentor

    Not necessarily. The graph is reflected across the x-axis when sin(x) < 0, which happens when -pi < x < 0, or when pi < x < 2pi, and a bunch of other intervals.
    That's how you need to look at it. It's not just when x >= 0 or x < 0.
     
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