convex concave sign in tkz-tab

Question

I'm a newby with both tkz-tab and tikz. I'd like to use tkz-tab to present the analysis of a function.

Is there a way to draw symbols for convex and concave that span over the whole diagram's cell, in the way the arrow are drawn ?

Up to now I've tried to use cup and cap symbols, but the result is not suitable. I would like to have something like a portion of a parabola.

Here is a mwe :

\documentclass{article}
\usepackage{tkz-tab}
\usepackage{amsmath,fullpage}
\begin{document}
\begin{tikzpicture}
\tkzTabInit[lgt=2,espcl=1]{
    $x$         /1,
    $\sin(x)$   /1
}% 
{
    $-\pi$, $0$ , $\pi$ 
}%
\tkzTabLine{  , {\Huge \smile} , t , \frown , }
\end{tikzpicture} 
\end{document}

Answer 1

One simple possibility, using \draw and some of the predefined nodes:

\documentclass{article}
\usepackage{tkz-tab}
\usetikzlibrary{calc}

\begin{document}

\begin{tikzpicture}
\tkzTabInit[lgt=2,espcl=1]{
    $x$         /1,
    $\sin(x)$   /1
}% 
{
    $-\pi$, $0$ , $\pi$ 
}%
\tkzTabLine{  , , t , , }
\draw[cyan,shorten >= 7pt,shorten <= 7pt] 
  ( $(T11)!0.2!(T12)$ ) to[out=-50,in=230,looseness=1.4] ( $(N21)!0.2!(N22)$ );
\draw[cyan,yscale=-1,shorten >= 7pt,shorten <= 7pt] 
  ( $(N22)!0.1!(N21)$ ) to[out=-50,in=230,looseness=1.4] ( $(T22)!0.1!(T21)$ );
\end{tikzpicture} 

\end{document}