$\begin{gathered} \cot 180=(\cos180)/(\sin180)=(-1)/(0)\colon\text{undefined} \\ \csc 180=(1)/(\sin 180)=(1)/(0)\colon\text{ undefined} \\ \cos 180=0 \\ \tan 180=(\sin 180)/(\cos 180)=(0)/(-1)=0 \\ \sec 180=(1)/(\cos 180)=(1)/(-1)=-1 \\ \sin 180=0 \end{gathered}$

As you can notice, cot180 and csc180 are undefined

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