Answer:
0
Step-by-step explanation:
The period of the function [tex]y=\tan x[/tex] is equal to [tex]\pi.[/tex]
To find the exact value of [tex]\tan (6\pi)[/tex], first note that we can skip 6 periods of this function, so
[tex]\tan (6\pi)=\tan 0[/tex]
Use definition of [tex]\tan:[/tex]
[tex]\tan 0=\dfrac{\sin 0}{\cos 0}[/tex]
Since
[tex]\sin 0 = 0\\ \\\cos 0=1,[/tex]
we have that
[tex]\tan (6\pi)=\tan 0=\dfrac{\sin 0}{\cos 0}=\dfrac{0}{1}=0[/tex]
