The discussion revolves around the domain of the tangent function, specifically addressing the set of values where the function is undefined. Participants explore the relationship between the mathematical definition of the domain and the graphical representation of the function.
Participants express differing views on the interpretation of the domain of tan x, with some agreeing on the mathematical definition while others question its implications based on graphical observations. The discussion remains unresolved regarding the clarity of the domain's representation.
There is an ongoing ambiguity regarding the definitions and implications of the domain and range of the tangent function, as well as the relationship between the mathematical representation and graphical behavior.
##\tan(x) = \frac{\sin(x)}{\cos(x)}## so whenever ##\cos(x) =0## then ##\tan(x)## isn't defined.shihab-kol said: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?
That set is the complement of the domain of the tan function -- the set of x values where tan x is undefined.shihab-kol said:I found in a book that the domain of tan x was {(2n+1)π/2 , n∈I}
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).shihab-kol said:So that set does not reflect the defined values of the function,just the undefined ones. Right?
Correct me if I am wrong.