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To typeset a value with a subscript I use this:
$U_{\text{res}}$
Which results in:
Now I'd like to write "the minimum value of Ures", how would I correctly typeset that?
The first thing I tried was
$U_{\text{res}_{\text{min}}}$
but that doesn't really look good. A coworker suggested
$U_{\text{res,min}}}$
but I'm also not sure if it's correct, and as part of a larger formula it seems to take up too much horizontal space:
I don't think there is a unique proper way of doing this.
There is the operator $\min$ which might be appropriate here.
In order to define your own operators, consider using \DeclareMathOperator{\Minimum}{Minimum} from amsmath to be able to use $\Minimum U_\mathrm{res}$. Using the operator will give you suitable spacing around the operator, just as you have with i.e. \sin.
\min in my own math convenience package :)
$U_{\mathrm{trig}} \geqslant blahbah$. And, in the first of the equalities you display, you might consider using \left(\right) around the first term of the product, so that, the braces expand according the size of what goes inside them.\text(though admittedly, in contrast with\mbox).\textis fine but heremaxis not a word it is essentially a math operator and should come from the math operator font to match\logor\sinetc and that will be the math roman font and not change depending on the outer text content.