# Domain of tan

• B
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?

fresh_42
Mentor
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?
##\tan(x) = \frac{\sin(x)}{\cos(x)}## so whenever ##\cos(x) =0## then ##\tan(x)## isn't defined.

jim mcnamara
jbriggs444
Homework Helper
2019 Award
I found in a book that the domain of tan x was {(2n+1)π/2 , n∈I}
That set is the complement of the domain of the tan function -- the set of x values where tan x is undefined.

So that set does not reflect the defined values of the function,just the undefined ones. Right?
Correct me if I am wrong.

jbriggs444
Mark44
Mentor
So that set does not reflect the defined values of the function,just the undefined ones. Right?
Correct me if I am wrong.
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).

jbriggs444