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Finding the range of values for tan theta > 1

  1. May 14, 2013 #1
    1. The problem statement, all variables and given/known data

    How to find the values of theta that make tan theta > 1 true?


    3. The attempt at a solution

    From trial and error I can find the solution to be 45 < theta < 90, but I was wondering if there was a systematic process to determining these values. I also know according to special triangles that tan45 = 1 but I dont know how that tells me the range, all that tells me is that tan theta ≠ 45. Is there a systematic process of finding the range of values?
     
  2. jcsd
  3. May 14, 2013 #2

    Mark44

    Staff: Mentor

    The tangent function is periodic with period ##\pi##. One interval for which tan(θ) > 1 is ##\pi/4 < \theta < \pi/2##. Can you figure out what all such intervals would be, given that the period is ##\pi##.

    Note that radian measure is used more often in mathematics than degree measure. ##\pi/4## = 45°.
     
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