The entire unit circle measures 2pi, then, pi corresponds to the half of the unit circle. It is located at the point (-1,0).
The cosine of pi is equal to the x-coordinate, and the sin of pi is equal to the y-coordinate of the point pi.
Since it is located at (-1,0) thus the cos(pi)=-1 and sin(pi)=0.
The functions that are undefined for pi are those which have sin(pi) as denominator, let's check:
[tex]\begin{gathered} \csc (\pi)=\frac{1}{\sin(\pi)}=\frac{1}{0}=undef \\ \cot (\pi)=\frac{\cos (\pi)}{\sin (\pi)}=\frac{-1}{0}=undef \end{gathered}[/tex]
