For coprime numbers $p$ and $q$, we consider the Vasyunin--cotangent sum $$ V(q,p)=um_{k=1}^{p-1}\Big\{\frac{kq}{p}\Big\}\cot\Big(\frac{i{k}}{p}\Big). $$ First, we prove explicit formula for the symmetric sum $V(p,q)+V(q,p)$ which is a new reciprocity law for the sums above. This formula can be seen as a complement to the Bettin--Conrey result \cite[Theorem 1]{BET1}. Second, we establish an asymptotic formula for $V(p,q)$. Finally, by use of continued fraction theory, we give a formula for $V(p,q)$ in terms of continued fraction of $\frac pq$.