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:
![\begin{gathered} \csc (\pi)=(1)/(\sin(\pi))=(1)/(0)=undef \\ \cot (\pi)=(\cos (\pi))/(\sin (\pi))=(-1)/(0)=undef \end{gathered}]()