1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Curve Sketching

  1. May 7, 2013 #1
    1. The problem statement, all variables and given/known data
    I need to find an x-intercept for this trigonometric equation, f(x)=(x/2)-sin(x). I already know that one of the intercepts in (0,0) because that is a y-intercept. I figure i could use Newton's method but this problem is in a section before Newton's method is introduced.


    2. Relevant equations



    3. The attempt at a solution
    I figured that the relation (sin(x)/x)=1 could possible be useful at first but now I know it's not. I know it has to be just one or two steps also. Help appreciated.
     
  2. jcsd
  3. May 7, 2013 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    If you are after an ##x## intercept instead of all of them, you are done because (0,0) is both an x and y intercept. Otherwise there is a root a bit less than 2 you will need Newton's method to find. And the function is odd, so...
     
  4. May 7, 2013 #3
    Sorry I forgot to put the interval, were only suppose to look at (0,3pi). This definitely brings up confusion for me. I thought I could only find the root using Newton's method but that is in a later section. But that is the only way right?
     
  5. May 7, 2013 #4

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You will need a numerical method of some sort. Maybe you are allowed to use a graphing calculator if you haven't studied Newton's method yet.
     
  6. May 7, 2013 #5
    I assume it must be a graphing calculator problem too. I do know how to use Newton's method,it just didn't make sense for someone that has studied only up to the chapter the problem is on. They must have just left the graphing calculator ok symbol out. But i used Newtons method and got the intercept, only to a couple decimal places though.
     
  7. May 7, 2013 #6

    Integral

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    You told us what you need to do, we need a complete problem statement so we can all work on the same thing.

    The title of the thread is "curve sketching", Have you sketched the curve? What tools for that do you have?
     
  8. May 7, 2013 #7
    Ohhh the problem is done and correctly sketched. It was a poor title now that I look at it. That one question was the part of the curve sketching I couldn't do without Newtons method or a calculator, that is what my question was. Sorry.
     
  9. May 8, 2013 #8

    Integral

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Try this, you have:

    [tex] F(x)= \frac x 2- Sin(x) [/tex]

    If you want the roots of this set [tex] F(x)=0= \frac x 2- Sin(x) [/tex]

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

    From your sketch you should know the number of roots and their approximate location. Make a rough estimate of a root, plug it into the RHS of the last equation get a new x, repeat several times.
     
    Last edited: May 8, 2013
  10. May 9, 2013 #9
    I like that. I just used straight forward Newton's method. I will work with this though, it makes for a more complete knowledge of what is going on with a graph.
     
  11. May 10, 2013 #10

    Integral

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Newton's method may converge faster then the above fixed point method, but it does converge after about 10 -12 iterations with an initial guess of .5. An initial guess of 2 took about 6 iterations.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Curve Sketching
  1. Sketch the Curve (Replies: 1)

  2. Curve Sketching (Replies: 2)

  3. Curve sketching (Replies: 6)

  4. Curve sketching (Replies: 6)

  5. Curve sketching (Replies: 2)

Loading...