Results 1 to 9 of 9

Math Help - Where the Graphs of two different equations intersect

  1. #1
    Newbie
    Joined
    Jun 2008
    Posts
    23

    Where the Graphs of two different equations intersect

    The Problem: I am given the graph y = sin x and  5 *\pi *y = 2x

    I am ask to find how many different points they intersect. I am literally blank when it comes to this question. I know solving for the system would give me one point where they intersect, but aside from graphing I have no idea as to how I would solve this.

    Could someone please help?

    Thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,741
    Thanks
    481
    solution by graphing is all you can do.

    \sin{x} - \frac{2x}{5\pi} = 0

    look for the roots.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    Quote Originally Posted by D. Martin View Post
    The Problem: I am given the graph y = sin x and  5 *\pi *y = 2x

    I am ask to find how many different points they intersect. I am literally blank when it comes to this question. I know solving for the system would give me one point where they intersect, but aside from graphing I have no idea as to how I would solve this.

    Could someone please help?

    Thank you.
    Another way is by iteration.
    For people like me who doesn't know how to use any graphing calculator, in graphing, and who doesn't know either how to graph in computers, the iteration method is a way.
    Search the Web for the Newton's Method, or the Newton-Raphson method for iteration, if you know some Calculus.

    Iteration is repetition. Trial and error. But there is a method whereby you know or can guess what value to try as you do repeated trials.

    Using my own iteration method,
    y = sin(x)
    y = 2x / 5pi
    ----------------
    sin(x) = 2x /5pi
    sin(x) -[2x /(5pi)] = 0 ----------try some x-values to get to zero.

    sin(x) is from -1.0 to 1.0 only, so try x's that would give (2x / 5pi) within (-1.0 to 1.0) only.

    I was getting x = 7.6 when I stopped iterating.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by ticbol View Post
    Another way is by iteration.
    For people like me who doesn't know how to use any graphing calculator, in graphing, and who doesn't know either how to graph in computers, the iteration method is a way.
    Search the Web for the Newton's Method, or the Newton-Raphson method for iteration, if you know some Calculus.

    Iteration is repetition. Trial and error. But there is a method whereby you know or can guess what value to try as you do repeated trials.

    Using my own iteration method,
    y = sin(x)
    y = 2x / 5pi
    ----------------
    sin(x) = 2x /5pi
    sin(x) -[2x /(5pi)] = 0 ----------try some x-values to get to zero.

    sin(x) is from -1.0 to 1.0 only, so try x's that would give (2x / 5pi) within (-1.0 to 1.0) only.

    I was getting x = 7.6 when I stopped iterating.
    indeed. but that is going to be REALLY painful here. there are 7 zeros (see graph below, the zeros that look like double roots are actually 2 roots), so to do an iteration for each is overkill. plus we have two pairs of roots where the zeros are very close to each other. that will make the guessing confusing
    Attached Thumbnails Attached Thumbnails Where the Graphs of two different equations intersect-graph.jpeg  
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    Quote Originally Posted by Jhevon View Post
    indeed. but that is going to be REALLY painful here. there are 7 zeros (see graph below, the zeros that look like double roots are actually 2 roots), so to do an iteration for each is overkill. plus we have two pairs of roots where the zeros are very close to each other. that will make the guessing confusing
    You only know those because you know how to graph on the computers and/or the graphing calculators. :-)
    Follow Math Help Forum on Facebook and Google+

  6. #6
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by ticbol View Post
    You only know those because you know how to graph on the computers and/or the graphing calculators. :-)
    exactly my point. it would take me forever to find them without this. this problem was probably made to be solved with some kind of CAS
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    Quote Originally Posted by Jhevon View Post
    exactly my point. it would take me forever to find them without this. this problem was probably made to be solved with some kind of CAS
    Okay, let's prolong this a bit.

    I did not say everything in my first reply to you, but the two curves,
    y = sin(x) ---------------a sine curve of amplitude 1.0
    and y = (2 / 5pi)x --------a straight line with positive slope,
    may not have seven intersection points.

    In fact, I guess there could only be one intersection point.

    Is that the graph of the y = sin(x) shown in your post? It's neutral axis is sloping downwards?
    If so, then, it is not okay.
    A sin curve, the basic one, has horizontal neutral axis.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by ticbol View Post
    Okay, let's prolong this a bit.

    I did not say everything in my first reply to you, but the two curves,
    y = sin(x) ---------------a sine curve of amplitude 1.0
    and y = (2 / 5pi)x --------a straight line with positive slope,
    may not have seven intersection points.

    In fact, I guess there could only be one intersection point.

    Is that the graph of the y = sin(x) shown in your post? It's neutral axis is sloping downwards?
    If so, then, it is not okay.
    A sin curve, the basic one, has horizontal neutral axis.
    no, i graphed the function \sin x - \frac {2x}{5 \pi}. the zeros of that graph are the x-values we seek

    the graph of both functions separately is below
    Attached Thumbnails Attached Thumbnails Where the Graphs of two different equations intersect-graph2.jpeg  
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    Quote Originally Posted by Jhevon View Post
    no, i graphed the function \sin x - \frac {2x}{5 \pi}. the zeros of that graph are the x-values we seek

    the graph of both functions separately is below
    Umm, now those graphs look familiar.
    So there really are 7 intersection points, according to exact graphings?

    Then, yes, to get all of the possible intersection points, computer assisted graphings is necessary.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Equations for the following graphs
    Posted in the Calculus Forum
    Replies: 3
    Last Post: August 2nd 2010, 05:55 AM
  2. Two sets intersect => their boundaries also intersect?
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: March 1st 2010, 02:23 PM
  3. Graphs and equations
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: February 12th 2009, 11:40 AM
  4. Find where the two graphs intersect.
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 16th 2008, 09:26 PM
  5. Replies: 4
    Last Post: September 5th 2007, 05:38 PM

Search Tags


/mathhelpforum @mathhelpforum