On using the slash to denote division in math mode

Question

In in-line math mode, I tend to use the literal slash (i.e. /) to denote division. Unlike the common binary operators [+ - \times \div], / is treated as an ordinary math object, though. This may easily result in inconsistent (asymmetric) horizontal spacing, for instance when / is preceded by a variable and succeeded by a function, as in the following example:

\documentclass{article}

\usepackage{amsmath}

\begin{document}

\noindent
\(\tan x = \sin x / \cos x\)

\end{document}

Output:

Of course, I can correct the horizontal spacing by turning \cos x into an ordinary math object:

\(\tan x = \sin x / {\cos x}\)

Output:

Alternatively, I can make / function as a binary operator similar to [+ - \times \div]:

\(\tan x = \sin x \mathbin{/} \cos x\)

Output:

Now, I am curious: Which of the above two workarounds should be preferred? Or is there even a better one?

Answer 1

You should definitely prefer the version \sin x / {\cos x} with the small spaces, or \sin x / \!\cos x as egreg suggests. From the TeXbook, page 132:

TeX does not treat / as a binary operation, even though a slash stands for division (which qualifies as a binary operation on mathematical grounds). The reason is that printers traditionally put extra space around the symbols +, −, and *, but not around /.

Knuth continues, explaining that 1 \mathbin{/} 2 would come out

which is wrong; so TeX considers / to be an ordinary symbol.

And from page 170:

In the formula $n/\log n$, TeX automatically inserts an unwanted thin space before \log, since the slash is treated as an ordinary symbol, and since a thin space is usually desirable between an ordinary symbol and an operator like \log.

Answer 2

In your case you use / as binary operator: \mathbin{/}:

$a \mathbin{/} b$

As an abbreviation a command could be defined to act as slash as binary operator:

\mathchardef\mslash="202F
$a \mslash b$

Or the symbol / can be changed globally to act as binary operator:

\mathcode`\/="202F
$a / b$

The starting number is the class, 0x200 is binary operator. The last two digits of the hexadecimal number 2F is the character code of /.

Answer 3

There are three LaTeX packages that seem to help: xfrac, nicefrac and (possibly) faktor (which last I have never looked at; there is a reference to it in the catalogue entry for nicefrac). Note that xfrac is a LaTeX-3-coded package.

It is possible that none of those help, but I would sooner use a tried-and-tested package than twiddle with the inner workings of maths mode (which generally makes me feel slightly ill).