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PLease HELP with this trigonometric equation

  1. Feb 2, 2007 #1
    Greetings my friends:
    I have been reading a book about optimization and I found the following trigonometric equation:
    tan(10x.pi)= - 10 pi x (this equation goes from x E [-1,2]
    it is easy to see that has infinite solutions, but the author came to the conclusion that the solutions are:
    xi=(2i-1)/20+Ei, for i=1,2,...


    xi=(2i+1)/20+Ei, for i=-1,-2,...

    HOw does he get those probable solutions, please I really need to know... :yuck:

    Thank you so much
  2. jcsd
  3. Feb 3, 2007 #2

    Gib Z

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    Homework Helper

    Welcome to Physicsforums.com!

    I may just be sleepy, but I cant see why its so obvious that there are an infinite number of solutions...let u=-10 pi x.

    we want solutions to tan(-u)=u, or -tan (u)=u. Since u=-10 pi x, and x E [-1,2], u E [-20pi, 10 pi]. It would have an infinite number of solutions if u E all R, but that is not the case.
  4. Feb 3, 2007 #3
    thank for the reply but I still have doubts

    Thank you for the reply, I will put the equation in a better wayat I do not know from where the author obtains the values of xi?????? :grumpy:
    why is it 2i-1/20 or the other way?
    Please help me
    Last edited: Feb 3, 2007
  5. Feb 3, 2007 #4
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