Y= l sin x l < absolute value of sinx

[Cudi1]

Homework Statement

y= l sin x l < absolute value of sinx

Homework Equations

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

 

[Mark44]

Homework Statement

y= l sin x l < absolute value of sinx

Homework Equations

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

What about the graph don't you get?

 

[Cudi1]

why are all y values above the x axis?

 

[eumyang]

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 |.

 

[Mark44]

That's what the absolute value does.

BTW, what you have here is incorrect -

y= l sin x l= sinx, if x>0
-sinx, if x< 0
0, if x=0

It should be
|sin x| = sin x, if sin x >= 0
-sin x, if sin x < 0

 

[Cudi1]

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)

 

[Mark44]

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.

 

[Cudi1]

y=sinx if sinx>=0 so if i input a value of 3pi/2, wouldn't that give me a negative number?

 

[Mark44]

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.

 

[Cudi1]

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

 

[Mark44]

k got it, so when x<0 it gets reflected across the x axis

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.

, 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

That's how you need to look at it. It's not just when x >= 0 or x < 0.