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B Domain of tan

  1. Nov 1, 2017 #1
    I found in a book that the domain of tan x was {(2n+1)π/2 , n∈I}
    The graph however shows that for every value of x , the function takes on a value .So, why is the domain like this?
  2. jcsd
  3. Nov 1, 2017 #2


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    Staff: Mentor

    ##\tan(x) = \frac{\sin(x)}{\cos(x)}## so whenever ##\cos(x) =0## then ##\tan(x)## isn't defined.
  4. Nov 1, 2017 #3


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    That set is the complement of the domain of the tan function -- the set of x values where tan x is undefined.
  5. Nov 2, 2017 #4
    So that set does not reflect the defined values of the function,just the undefined ones. Right?
    Correct me if I am wrong.
  6. Nov 2, 2017 #5


    Staff: Mentor

    The set you wrote in post #1 is not the defined values of the function. The range of the tangent function (set of all output values) is all real numbers. That set in post #1 lists (by a formula) all of the numbers that are not in the domain of tan(x).
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