0

How to arrange the equation sideway in the margin?

\documentclass{scrartcl}
\usepackage[showframe,
            textwidth=8cm,
            textheight=5cm]{geometry}
\usepackage{mathtools}
\usepackage{marginnote}

\begin{document}
\noindent X\dotfill X
%
\begin{align*}
  \sin^2 \theta &= 1-\cos^2 \theta\marginnote{$\cos^2\theta+\sin^2\theta=1$ } \\
  c &= d 
\end{align*} 
\end{document}
1

You can use \rotatebox (see the grfguide for more information) to rotate the equation, e.g.,

\documentclass{scrartcl}
\usepackage[showframe,
            textwidth=8cm,
            textheight=5cm]{geometry}
\usepackage{mathtools}
\usepackage{marginnote}

\begin{document}
\noindent X\dotfill X
%
\begin{align*}
  \sin^2 \theta &= 1-\cos^2 \theta\marginnote{\rotatebox{90}{$\cos^2\theta+\sin^2\theta=1$ }} \\
  c &= d 
\end{align*}

\end{document}

page with rotated equation in margin

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