In radians, pi is equal to 180º
Then, for each pi, we add 180º. we know that sin(pi) = 0 and cos(pi) = -1
Then:
[tex]7\pi=7\cdot180º=180º+180º+180º+180º+180º+180º+180º[/tex]
but, we can see that 180º + 180º = 360º = 0º
Then, all we need to know is the value of the trigonometric functions at pi (in this case, it's the same 7pi or -7pi)
Thus:
[tex]\begin{gathered} \cos (\pi)=-1 \\ \sin (\pi)=0 \\ \tan (\pi)=\frac{\sin(\pi)}{\cos(\pi)}=\frac{0}{-1}=0 \\ \cot (\pi)=\frac{1}{\tan(\pi)}=\frac{\cos (\pi)}{\sin (\pi)}=\frac{-1}{0}=\text{undefined} \\ \sec (\pi)=\frac{1}{\cos (\pi)}=\frac{1}{-1}=-1 \\ \csc (\pi)=\frac{1}{\sin(\pi)}=\frac{1}{0}=\text{ undefined} \\ \\ \end{gathered}[/tex]
