Use the graph of \(y~=~\cot(x)\) on \((0,~\pi~)\) to state the period, all zeros, vertical asymptotes, defined branches, monotonic direction and end behavior on each full branch, and range.

Use cotangent's quotient form to separate its two landmark types: denominator zeros produce excluded asymptotes, while numerator zeros produce graph zeros when the denominator remains nonzero. Adjacent asymptotes bound one complete branch, so its width reveals the period. Reading that branch from one boundary to the other gives its direction, end behavior, and range.