The domain of the tangent function, tan(x), is defined as the set of values where the function is undefined, specifically at {(2n+1)π/2, n∈I}, due to the cosine function equating to zero at these points. The tangent function is expressed as tan(x) = sin(x)/cos(x), indicating that it is undefined whenever cos(x) = 0. The discussion clarifies that this set represents the complement of the domain, meaning it lists the x-values where tan(x) does not exist, while the range of tan(x) encompasses all real numbers.
PREREQUISITESStudents of mathematics, educators teaching trigonometry, and anyone seeking to deepen their understanding of the properties of the tangent function and its graphical representation.
##\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.