New cup and cap symbol

Question

I'm redrawing these symbols (don't ask why :)) How can I draw them more properly?

(Circle and line segments do not exactly intersect)

My Code:

\documentclass[a4paper]{article}
\usepackage[margin=1.5cm]{geometry}
\usepackage{amsmath}
\usepackage{tikz}

\newcommand{\mycupsymbol}{     
\hspace{1.1mm}\tikz[baseline, line width=0.6 pt, line cap=round]{
  \draw (1.103,0.08) -- ++(0,0.15);
  \draw (0.903,0.08) -- ++(0,0.15);
  \draw (1.103,0.08) arc (0:-180:0.1);
}
\hspace{1.1mm}}
\newcommand{\mycup}{\mycupsymbol}

\newcommand{\mycapsymbol}{     
\hspace{1.1mm}\tikz[baseline, line width=0.6 pt, line cap=round]{
  \draw[line width=0.581] (1.1033,-0.022) -- ++(0,0.15);
  \draw[line width=0.581] (0.9033,-0.022) -- ++(0,0.15);
  \draw (1.103,0.13) arc (0:180:0.1);
}
\hspace{1.1mm}}
\newcommand{\mycap}{\mycapsymbol}


\begin{document}

$$A_2\mycup \mycap S_2$$

\end{document}

Answer 1

A couple of suggestions:

1. It's better to use scalable units w.r.t. the font (ex as in my example, or em).
2. Draw all the paths with only one \draw, it's easier this way.
3. Create only one macro (\mysymbol in my case) with a parameter and rotate it.
4. Define before the macro variables with all the dimensions involved. This way it's easy to modify until you have exactly what you need.

That said, this is my example, edited as suggested by egreg in the comments. Previously there could be conflicts with the names of the macros. I also changed \def for \newcommand to make this macros.

\documentclass[a4paper]{article}
\usepackage{tikz}

\newcommand\myheight{1.5ex} % cup and cap height
\newcommand\mywidth {1.2ex} % cup and cap width
\newcommand\mylinew {0.1ex} % cup and cap line width
\newcommand\spaceba {0.4ex} % space before and after
\newcommand{\mysymbol}[1]
{
  \hspace{\spaceba}
  \tikz[line width=\mylinew,line cap=round,rotate=#1]
    \draw (0,\myheight) -- (0,0.5*\mywidth) arc (-180:0:0.5*\mywidth) -- (\mywidth,\myheight);
  \hspace{\spaceba}
}
\newcommand{\mycup}{\mysymbol{0}}
\newcommand{\mycap}{\mysymbol{180}}

\begin{document}
\[A_2\mycup \mycap S_2\]
\huge
\[A_2\mycup \mycap S_2\]
\end{document}

And the output: