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Graphical solution to an equation relating tan(x) to a semi semi circle

  1. Oct 17, 2012 #1
    1. The problem statement, all variables and given/known data
    Using graphical means, determine how many positive roots exist, as a function of a, the the following equation.


    2. Relevant equations
    √(a2-x2) = tan(x)


    3. The attempt at a solution

    I've sketched graphs showing tan(x) and the semi circle overlapping for various radii. Obviously at the radius increases the number of roots increases but I have no idea how to find a relationship between them. Any help would be awesome!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 18, 2012 #2

    ehild

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    Homework Helper
    Gold Member

    What is the domain of sqrt(a2-x2)? How far does it extend along the x axis?
    How many tangent curves are there in that interval?

    ehild
     
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