# Problem with arithmetic of rotations in pdfpages

There is an arithmetic or interface problem with the package pdfpages. Let us include a scan from a book:

% !TEX TS-program = pdflatex

\documentclass[11pt]{book}
\usepackage{pdfpages}

\begin{document}
\includepdf[pages = 1, scale = 0.10, offset = 0mm 0mm, angle =  0.90 ]{scan1}
\includepdf[pages = 1, scale = 0.56, offset = 0mm 0mm, angle = -0.9  ]{scan2}
\end{document}

The correct angle to include scan2 is -0.9.

— If the angle of the first include is different of 0.9 as a string (by example, 0.90), the inclusion of scan2 is OK (the lines do not belong to the scan) :

— But if the angle of the first include is 0.90 as a string, then the orientation of scan2 is wrong :

• Interesting. pdfpages is not at fault, the problem exists also with graphicx and looks like a tex core problem. \number -0.9 \relax outputs 0.9 and so the second image reuses the angle calculation of the first. – Ulrike Fischer Aug 17 '16 at 12:19
• After a discussion in the chat I think the problem is with trig.sty. – Ulrike Fischer Aug 17 '16 at 12:32

The problem is that trig uses \number#1 to force the decimal expansion of the value (which might be a register or chardef token) but \number-0.9 is 0.9 as \number only sees the integer part and 0=-0.

You can force the correct interpretation of sin as below (or more simply just add (say) 360 to the value so it isn't a value between 0 and -1 which is the only range that fails)

\documentclass{article}
\usepackage{graphicx}
\makeatletter
\def\UseSin#1{\csname sin(\ifdim#1\p@<\z@-\number-#1\else\number#1\fi)\endcsname}
\def\UseCos#1{\csname cos(\ifdim#1\p@<\z@-\number-#1\else\number#1\fi)\endcsname}

\CalculateSin{0.9}
\CalculateCos{0.9}
\typeout{A: \UseSin{0.9},\UseCos{0.9}}
\expandafter\xdef\csname sin(-0.9)\endcsname{-\UseSin{0.9}}
\expandafter\xdef\csname cos(-0.9)\endcsname{\UseCos{0.9}}
\expandafter\xdef\csname sin(-0.91)\endcsname{-\UseSin{0.91}}
\expandafter\xdef\csname cos(-0.91)\endcsname{\UseCos{0.91}}

\typeout{B: \UseSin{-0.9},\UseCos{-0.9}}

\begin{document}

\includegraphics[scale = 0.50, angle =  0.9 ]{example-image-a}
\includegraphics[scale = 0.50, angle = -0.9 ]{example-image-b}

\includegraphics[scale = 0.50, angle =  0.910 ]{example-image-a}
\includegraphics[scale = 0.50, angle = -0.91 ]{example-image-b}

\end{document}

I'll see if I can think of a better fix to add to trig...