Why does \usepackage[T2A]{fontenc} take over?

Question

I want to produce a document with non-serif type. I also want to include Cyrillic characters. These two aims seem to be mutually exclusive. When I comment out \usepackage[T2A]{fontenc}, the document is beautiful, except that the Cyrillic characters won't print. When I include \usepackage[T2A]{fontenc}, the document is beautiful, but it is entirely a serif font.

Below is a MWE. Some of the preamble might seem a little bit goofy, but it's all included in my university's template (see link below). It will actually compile, but only with some encouragement (see http://helpdesk.ufl.edu/wp-content/uploads/2012/12/latex_spring_2011.zip).

From what I've read, I think I need to load a different font family. But I'm not sure if that's right, or even how to do it.

How do I have a document that both includes Cyrillic characters and retains its sans serif font?

\documentclass{article}
\renewcommand{\rmdefault}{ma1}
\renewcommand{\sfdefault}{phv}
\renewcommand{\familydefault}{\sfdefault}
\usepackage{datetime}
\usepackage{qtree}
\usepackage[T1,T2A]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{tipa}
\usepackage{pgfplots}
\usepackage[authoryear]{natbib}
\usepackage{hypernat}
\usepackage[dvipdfm,hyperfootnotes=false]{hyperref}
\hypersetup{colorlinks=true,linkcolor=blue,anchorcolor=blue,citecolor=blue,filecolor=blue,urlcolor=blue,bookmarksnumbered=true,pdfview=FitB} \usepackage{gb4e}
\noautomath
\let\eachwordone=\sffamily
\let\eachwordtwo=\sffamily
\let\eachwordthree=\sffamily

\begin{document}

Todd is a cat. у меня есть машина. я очень харашо.

\end{document}

Answer 1

TeX fonts have only 256 slots. And you can't mix encodings without telling LaTeX to do it; \textcyrillic defined by babel with the russian option does this. The last specified encoding becomes the default one.

---

This should be a complete list of sans serif fonts available also in T2A encoding (for cyrillic):

\documentclass{article}
\usepackage[T2A,T1]{fontenc}
\usepackage[utf8]{inputenc}

\usepackage[russian,english]{babel}

\renewcommand{\familydefault}{\sfdefault}


\begin{document}

\renewcommand{\sfdefault}{PTSans-TLF}\normalfont
\section{PTSans}

Todd is a cat. \textcyrillic{у меня есть машина. я очень харашо.}


\renewcommand{\sfdefault}{fds}\normalfont
\section{Droid}

Todd is a cat. \textcyrillic{у меня есть машина. я очень харашо.}


\renewcommand{\sfdefault}{fco}\normalfont
\section{Comforta}

Todd is a cat. \textcyrillic{у меня есть машина. я очень харашо.}


\renewcommand{\sfdefault}{fca}\normalfont
\section{Cantarell}

Todd is a cat. \textcyrillic{у меня есть машина. я очень харашо.}


\renewcommand{\sfdefault}{iwona}\normalfont
\section{Iwona}

Todd is a cat. \textcyrillic{у меня есть машина. я очень харашо.}


\renewcommand{\sfdefault}{fos}\normalfont
\section{OpenSans}

Todd is a cat. \textcyrillic{у меня есть машина. я очень харашо.}

\end{document}

Of course the declarations should be given in the preamble, this is just to show the specimens.

With the following example, I show the result of having Helvetica (Arial is similar) for Latin text and one of the previous fonts for Russian text in cyrillic. Take your pick and define \sfcyrillic to the chosen family.

\documentclass{article}
\usepackage[T2A,T1]{fontenc}
\usepackage[utf8]{inputenc}

\usepackage[russian,english]{babel}

\renewcommand{\sfdefault}{phv}
\renewcommand{\familydefault}{\sfdefault}

\newcommand{\sfcyrillic}{} %%% Add here your preference
\usepackage{xpatch}
\xpatchcmd{\Russian}
  {\selectfont}
  {\fontfamily{\sfcyrillic}\selectfont}
  {}{}
\xshowcmd\Russian


\begin{document}

\renewcommand{\sfcyrillic}{PTSans-TLF}\normalfont
\section{PTSans}

Todd is a cat. \textcyrillic{у меня есть машина. я очень харашо.}


\renewcommand{\sfcyrillic}{fds}\normalfont
\section{Droid}

Todd is a cat. \textcyrillic{у меня есть машина. я очень харашо.}


\renewcommand{\sfcyrillic}{fco}\normalfont
\section{Comforta}

Todd is a cat. \textcyrillic{у меня есть машина. я очень харашо.}


\renewcommand{\sfcyrillic}{fca}\normalfont
\section{Cantarell}

Todd is a cat. \textcyrillic{у меня есть машина. я очень харашо.}


\renewcommand{\sfcyrillic}{iwona}\normalfont
\section{Iwona}

Todd is a cat. \textcyrillic{у меня есть машина. я очень харашо.}


\renewcommand{\sfcyrillic}{fos}\normalfont
\section{OpenSans}

Todd is a cat. \textcyrillic{у меня есть машина. я очень харашо.}

\end{document}

Answer 2

To complement egreg's more accurate answer for latex, you might want to look into xelatex, which supports every package from latex that I have ever tried (and more!). You would just need to change your typesetting engine.

Here is the code to achieve what you want with the fewest lines possible.

Loading a new font family is easy:

\setmainfont{nameofsystemfont}

I chose (reluctantly) Arial for this example, but any font that contains both cyrillic characters and latin characters will suffice.

UPDATED CODE TO INCLUDE POLYGLOSSIA AS PER EGREG'S COMMENT

\documentclass[12pt]{article}
\usepackage{fontspec}
\usepackage{polyglossia} %% added for proper hyphening
\setmainfont{Arial}
\begin{document}

Todd is a cat. у меня есть машина. я очень харашо.

\end{document}

Also check out What fonts can I use for writing in Cyrillic in LaTeX