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Homework Help: What is the domain of tan(x/b)?

  1. Nov 10, 2009 #1
    1. The problem statement, all variables and given/known data

    What is the domain for tan(x/b)?

    2. Relevant equations

    3. The attempt at a solution
    tan(x) domain is all real number , except x=[tex]\pi/2[/tex]+n pi nEI
    tan(x/b)will be bpi/2+bnpi? Is there any form i can write?
    Am i right? Thanks
    Last edited: Nov 10, 2009
  2. jcsd
  3. Nov 10, 2009 #2


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    Science Advisor
    Homework Helper
    Gold Member

    Yes. You could write D ={ b(π/2 + nπ) | n ε I}
  4. Nov 12, 2009 #3
    But my teacher said the answer is wrong,
    the right answer is bn(pi/2), Can anyone explain it?
  5. Nov 12, 2009 #4


    Staff: Mentor

    I think your teacher is wrong. For example, assuming for the moment that b is an integer, if n = 2, 2b*pi/2 = b*pi. tan(2b*pi/2) = tan(b*pi) = 0.

    The domain of tan(x) is all reals except odd multiples of pi/2. The tangent function is defined at x = +/-pi, +/-2pi, +/-3pi, etc., but is undefined at x = +/-pi/2, +/-3pi/2, +/-5pi/2.

    The graph of y = tan(x/b) is the expansion away from the y axis of the graph of y = tan(x) by a factor of b, whether or not b is an integer. So tan(x/b) will be undefined at x = +/-b*pi/2, +/-b*3pi/x, +/-b*5pi/x, etc. The domain is all reals except odd multiples of b*pi/2.
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