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Homework Help: Range of a trigonometric function

  1. Nov 20, 2007 #1
    1. The problem statement, all variables and given/known data

    Find the range of the function: y=(2cosx+1)/(2cosx-1) algebraically

    2. Relevant equations

    Reducing it, I obtained: y= tan(3x/2)/tan(x/2), but the discontinuity confuses me

    3. The attempt at a solution

    I did it with my calculator and this is the result:

    Ran = (-oo,1/3] U [3,+oo) but I hope I can get help with the algebraic solution.

    Thanks in advance.
  2. jcsd
  3. Nov 20, 2007 #2


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    Staff Emeritus
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    Gold Member

    The discontinuity is quite useful, as that informs you that the range of the function reaches infinity and minus infinity. If cosx=1/2, then x=pi/6(along with a variety of other numbers). 2cos(pi/6)+1=2. So we have something like 2/e, where e is a small number, when x is near pi/6. If x is less than pi/6, e is negative, and can be arbitrarily small. If x is greater than pi/6, e is positive and arbitrarily small. So if e is negative, it goes to negative infinity, if e is positive it goes to positive infinity.

    It's similiar to how the graph of 1/x works
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