  We answer a question raised by Misiurewicz and Rodrigues concerning the
family of degree 2 circle maps $F_\lambda:\mathbb{R}/\mathbb{Z}\to
\mathbb{R}/\mathbb{Z}$ defined by \[F_\lambda(x) := 2x + a+ \frac{b}{\pi}
\sin(2\pi x){\quad\text{with}\quad} \lambda:=(a,b)\in
\mathbb{R}/\mathbb{Z}\times (0,1).\] We prove that if $F_\lambda^{\circ n}-{\rm
id}$ has a zero of multiplicity $3$ in $\mathbb{R}/\mathbb{Z}$, then there is a
system of local coordinates $(\alpha,\beta):W\to \mathbb{R}^2$ defined in a
neighborhood $W$ of $\lambda$, such that $\alpha(\lambda) =\beta(\lambda)=0$
and $F_\mu^{\circ n} - {\rm id}$ has a multiple zero with $\mu\in W$ if and
only if $\beta^3(\mu) = \alpha^2(\mu)$. This shows that the tips of tongues are
regular cusps.
