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

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Homework Help Overview

The problem involves determining the domain of the function tan(x/b), where b is a parameter. Participants are exploring the implications of the tangent function's properties and how they relate to the variable b.

Discussion Character

  • Conceptual clarification, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to establish the domain based on the known properties of the tangent function, questioning whether the domain can be expressed in a specific form. Other participants engage in verifying or challenging the correctness of the proposed domain.

Discussion Status

The discussion is active, with differing opinions on the correct domain. Some participants provide alternative perspectives and reasoning, while others express uncertainty about the teacher's assertion regarding the domain.

Contextual Notes

There is mention of potential constraints regarding the value of b, with some participants assuming it could be an integer. The discussion highlights the importance of understanding the behavior of the tangent function at specific points.

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Homework Statement



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

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