1. Limited time only! Sign up for a free 30min personal 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!

Trigonometric Equations

  1. May 22, 2007 #1
    How would one go about solving sin(x) = x/2
    I.e. the intersections of

    I can rigorously solve this by going to each individual period and finding the intersections. But is there a better way?
  2. jcsd
  3. May 22, 2007 #2
    You can find the no. of solutions easily enough using graphs, but getting the actual solution, would require rigour.
  4. May 22, 2007 #3
    This is going to do my scholarship exam on Friday. I was only notified today that I was selected. Although I knew most of the requirements prior to this, I did not know about trigonometric equations such as this. I cannot afford to draw graphs - time constraints are not going to do me favours. I know for sin(x)=k, there is a simple general solution rule. But as for kx; are there any quicker methods?
  5. May 23, 2007 #4
    Do you want to know the exact intersections or the number of intersections? If it's the number, it's fairly easy. The maxima and minima of sin x all have y = 1 and y = -1. The function x/2 is equal to 1 at x = 2 and - 1 at x = -2. Since the pi/2< 2 <pi, then it has to cross sin x at two points on the positive x axis (picture this in your mind: the line has to cross the "mountain" between 0 and pi). Same applies to -2 > -pi. There are in total 3 intersection points (x = 0 is common to the positive and negative sides of the x axis).
  6. May 23, 2007 #5
    Yes I suppose knowing the number of solutions may be helpful. However, the values are also expected...
  7. May 23, 2007 #6
    Then, there exist no analytical method. Apart from the obvious x = 0 solution, the others have to be found by other method. Are you familiar with Newton's method?
  8. May 23, 2007 #7
    No I am not aware of Newton's method
  9. May 23, 2007 #8
    Then learn about it, you haven't got much time! Though, it's strange that they would ask you this kind of question...
    Last edited: May 23, 2007
  10. May 23, 2007 #9
    Wow! I have just learnt it! It is quite accurate with just 3 steps. Since they expect 3 s.f. it is perfect. Thanks.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook