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Very basic precal question about cotangent and tangent

  1. Mar 19, 2009 #1
    So, I just learned in class that to get inverse cot-1(x) I have to do tan-1(1/x). Then add either pi, or 180 depending on wheather we are using radians or degrees.

    And I don't understand this. If x is cot, then when we do 1/x, shouldn't we get tan? And after than isn't it enough to just do tan-1(1/x) to get the answer? What is the point of adding that pi or 180 degrees?
     
  2. jcsd
  3. Mar 19, 2009 #2

    tiny-tim

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    Hi Ghost803! :smile:

    That only applies to negative values of x.

    It all depends on the definition of principal value.

    For tan, the principal value is between ± π/2 (because tan = ±∞ at ±π/2)

    but for cot, the principal value is between 0 and π (because cot = ±∞ at 0 and π).

    (see http://en.wikipedia.org/wiki/Inverse_trigonometric_functions)

    So for cot-1(x) for negative x, tan-1(1/x) would be < 0, which is not a principal value for cot, so you have to add π :wink:
     
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