Can siunitx use roman when familydefault is set to sans serif? [duplicate]

Question

Possible Duplicate:
Can I make siunitx commands use serif fonts like the rest of the math in beamer?

I have a MWE showing setting the family default to sans serif with \renewcommand{\familydefault}{\sfdefault}. When this is done, no matter what settings to siunitx I have tried to use (shown in the example), I can't get the math modes ($$ and \[\]) to display units and numbers in the roman serif font.

\documentclass[12pt]{article} % use larger type; default would be 10pt
\renewcommand{\familydefault}{\sfdefault}
\usepackage{siunitx}
\sisetup{detect-mode=false,detect-family=false,
        detect-display-math=false,detect-shape=false,
        mode=math}

\begin{document}
text where you have \SI{450}{\volt}\\
$\textrm{inline math} \quad \sin^2(x) \quad \SI{450}{\volt}\\
\textrm{textrm V}$
\[\textrm{math environment}\quad \SI{450}{\volt}\]
\end{document}

The result is

Ideally, I would expect the units given in text to be typeset in sans serif (even though this is considered naughty by SI standards), and the units inside $$ or \[\] to be typeset in roman or whatever the current math font is.

I have noticed that it can get halfway there if you use \sfseries instead of \familydefault, meaning that text and $$ will be typeset sans serif, while \[\] can be typeset roman. That solution is a problem for my documents, since I use sans serif for section headings as well.

Answer 1

Joseph pointed me in the right direction with this question Can I make siunitx commands use serif fonts like the rest of the math in beamer?. Beyond adding the \AtBeginDocument as recommended there, I changed text-rm=\rmfamily to text-rm=\sffamily to get sans serif mid text, then removed the mode setting and changed detect-mode=true.

\documentclass[12pt]{article} % use larger type; default would be 10pt
\renewcommand{\familydefault}{\sfdefault}
\usepackage{siunitx}
\sisetup{detect-mode=true,detect-family=false,
        detect-display-math=false,detect-shape=false}
\AtBeginDocument{\sisetup{math-rm=\mathrm, text-rm=\sffamily}}


\begin{document}
text where you have \SI{450}{\volt}\\
$\textrm{inline math} \quad \sin^2(x) \quad \SI{450}{\volt}\\
\textrm{textrm V}$
\[\textrm{math environment}\quad \SI{450}{\volt}\]
\end{document}