Verified answer

T - период функции

[tex]\displaystyle\bf\\1)\\\\y=tg\pi x\\\\k=\pi \ \ \ \Rightarrow \ \ \ T=\frac{\pi }{\pi } =1\\\\\\2)\\\\y=Cos\frac{\pi x}{6} \\\\k=\frac{\pi }{6} \ \ \ \Rightarrow \ \ \ T=\frac{2\pi }{\frac{\pi }{6} } =12\\\\\\3)\\\\y=Sin2x\\\\k=2 \ \ \ \Rightarrow \ \ \ T=\frac{2\pi }{2} =\pi \\\\\\4)\\\\y=2Cos\frac{x}{3}-4 \\\\k=\frac{1}{3} \ \ \ \Rightarrow \ \ \ T=\frac{2\pi }{\frac{1}{3} } =6\pi[/tex]