Solution:
Given:
[tex]f(t)=tan\text{ }t[/tex][tex]\begin{gathered} when\text{ }t=-\frac{\pi}{2} \\ f(t)=tan(-\frac{\pi}{2}) \\ f(t)=undefined \\ \\ \\ when\text{ t}=-\frac{\pi}{3} \\ f\mleft(t\mright)=tan(-\frac{\pi}{3}) \\ f(t)=-\sqrt{3} \\ \\ \\ when\text{ t}=-\frac{\pi}{4} \\ f\mleft(t\mright)=tan(-\frac{\pi}{4}) \\ f(t)=-1 \\ \\ \\ when\text{ t}=-\frac{\pi}{6} \\ f\mleft(t\mright)=tan(-\frac{\pi}{6}) \\ f(t)=-\frac{\sqrt{3}}{3} \end{gathered}[/tex]
[tex]\begin{gathered} when\text{ }t=0 \\ f(t)=tan(0) \\ f(t)=0 \\ \\ \\ when\text{ t}=\frac{\pi}{6} \\ f\mleft(t\mright)=tan(\frac{\pi}{6}) \\ f(t)=\frac{\sqrt{3}}{3} \\ \\ \\ when\text{ t}=\frac{\pi}{4} \\ f\mleft(t\mright)=tan(\frac{\pi}{4}) \\ f(t)=1 \\ \\ \\ when\text{ t}=\frac{\pi}{3} \\ f\mleft(t\mright)=tan(\frac{\pi}{3}) \\ f(t)=\sqrt{3} \\ \\ \\ when\text{ t}=\frac{\pi}{2} \\ f\mleft(t\mright)=tan(\frac{\pi}{2}) \\ f(t)=undefined \\ \\ \\ when\text{ t}=\frac{2\pi}{3} \\ f\mleft(t\mright)=tan(\frac{2\pi}{3}) \\ f(t)=-\sqrt{3} \end{gathered}[/tex]
Therefore, the complete table is;
