Use text font for alphanumeric characters in math

Question

My document currently uses TeX Gyre Termes as the main text font and Computer Modern for math. I would like to continue using Computer Modern for math mode symbols, operators, and greek, but replace the normal roman and italic alphanumeric characters (a-z A-Z 0-9) with the corresponding ones from the text font.

In short, I would like to go from the above equation to the below equation.

The code for the mockup perhaps helps to illustrate the point further:

I would like to go from this,
\begin{equation}
    2 \, \alpha \, v \begin{pmatrix}
        \cos(t) \\
        \sin(t)
    \end{pmatrix} \;,
\end{equation}
to this,
\begin{equation}
    \mbox{2} \, \alpha \, \mbox{\textit v} \begin{pmatrix}
        \mbox{cos}(\mbox{\textit t}) \\
        \mbox{sin}(\mbox{\textit t})
    \end{pmatrix}\;.
\end{equation}
As you can see, the number 2, the italic ``\textit{v}'' and ``\textit{t}'', and
the upright ``cos'', ``sin'' are taken from the main text font.

Unfortunately, I do not know the correct terminology to refer to these different types of fonts, which makes searching for a solution that much harder.

Answer 1

By chance, I found the answer in a comment to an unrelated question.

There is a mathastext package that

uses a text font (usu­ally the doc­u­ment’s text font) for the let­ters of the Latin al­pha­bet needed when type­set­ting math­e­mat­ics. (Op­tion­ally, other char­ac­ters in the font may also be used).

There are a number of examples available in the showcase.