1. You have the function [tex] y=tan(\frac{x}{8} ) [/tex]
2. You know that [tex] y=\frac{sinx}{cosx} [/tex] with [tex] cosx\neq 0 [/tex], because the division by zero is not defined. So , [tex] cosx=0 [/tex] for [tex] \frac{(2n+1)\pi}{2} [/tex] where [tex] n [/tex] is a integer number.
3. Then, to find the domain of the function given in the problem, you must make [tex] \frac{x}{8} \neq \frac{k\pi}{2} \\ x\neq 4k\pi [/tex]
Where [tex] k [/tex] is odd number.
4. Therefore:
[tex] x\neq 4\pi (2n+1) [/tex]
5. Finally, the domain is: [tex] 4\pi (2n+1)<x<4\pi (2n+3) [/tex]
The answer is: [tex] 4\pi (2n+1)<x<4\pi (2n+3) [/tex]
