documentclass[letterpage,12pt]{book}

usepackage{amsmath,amsthm,amssymb}
DeclareMathSizes{12}{12}{6}{6}
%everymath{displaystyle}

%https://www.physicsforums.com/threads/script-lowercase-r-in-latex.450030/
% Declares the font
usepackage{calligra}
DeclareMathAlphabet{mathcalligra}{T1}{calligra}{m}{n} DeclareFontShape{T1}{calligra}{m}{n}{<->s*[2.2]callig15}{}
% Makes 'sr' make a script r
newcommand{sr}{ensuremath{mathcalligra{r}}}

begin{document}

begin{equation*}
    mathrm{R}^2 = r^2 + sr^2 - 2r sr cosomega
end{equation*}

end{document}