Finding the Intersection of Graphs for Homework Equation

The conversation is about finding the value of x that satisfies the equation 1 = absolute value( (sin(x)-x)/(sin(x))) * 100. The person attempted to solve it graphically and obtained a value of x = 0.244 radians as the intersection point, but is unsure if it is correct due to being able to manipulate the equation to make it never intersect or change the intersection point. They then mention using Mathematica to find the root and getting a value of x = 0.244097, which makes sense.
  • #1
MrXow
60
0

Homework Statement


1 = absolute value( (sin(x)-x)/(sin(x))) * 100


Homework Equations


Don't think there are any.


The Attempt at a Solution


I decided to do it graphically, so i graphed y=.01 and y= absolute value(1-(x/sin(x))
I got x = .244 radians for the intersection and I am just not sure if it is correct because i can manipulate the equation so that they never intersect or I can manipulate it so the point changes.
 
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  • #2
Be more specific. How did you manipulate the equation?
 
  • #3
MrXow said:

Homework Statement


1 = absolute value( (sin(x)-x)/(sin(x))) * 100


Homework Equations


Don't think there are any.


The Attempt at a Solution


I decided to do it graphically, so i graphed y=.01 and y= absolute value(1-(x/sin(x))
I got x = .244 radians for the intersection and I am just not sure if it is correct because i can manipulate the equation so that they never intersect or I can manipulate it so the point changes.

In order to see the problem better..

[tex] 1= |(\frac{\sin(x)-x}{\sin(x)})(100)| [/tex]
 
  • #4
ya that's it I don't know how to do that fancy typing stuff
 
  • #5
when i put it in mathematica
"FindRoot[1 == Abs[((Sin[x] - x)/Sin[x])]*100, {x, 0.1}]"
i get
{x -> 0.244097}
which makes sense
 
  • #6
So, what is your question?
 

1. How do I find the intersection of two graphs for a homework equation?

To find the intersection of two graphs, you need to set the two equations equal to each other and solve for the variable. The resulting value will be the x-coordinate of the intersection point. Then, plug in this value into either of the original equations to find the y-coordinate. This will give you the point of intersection for the two graphs.

2. Can I use a graphing calculator to find the intersection of two graphs?

Yes, most graphing calculators have a function to find the intersection of two graphs. Simply input the two equations and the calculator will give you the coordinates of the intersection point.

3. What if the graphs do not intersect?

If the graphs do not intersect, it means that there is no solution to the equation. This could happen if the equations represent parallel lines or if they represent two different functions with no common points.

4. Is there a shortcut method for finding the intersection of two graphs?

Yes, some equations can be solved for the intersection point by manipulating the equations in a certain way. For example, if one equation is in the form of y = mx + b and the other is in the form of ax + by = c, you can substitute the first equation into the second to solve for the x-coordinate of the intersection point.

5. How do I check if my answer for the intersection point is correct?

To check if your answer is correct, plug the coordinates of the intersection point into both original equations. If the resulting values are equal, then your answer is correct. Additionally, you can graph the two equations and see if the point you found lies on both graphs.

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