%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% macros to calculate sines from 90 to -90
% Jim Walker, Dept Mathematics, University of South Carolina
\newdimen\x
\newdimen\y
\newdimen\xsquare
\newdimen\xfourth
{% change char codes
\catcode`\p=12
\catcode`\t=12
\gdef\numonly#1pt{%
\def\xx{#1}%
}%
}%
\def\MULTyBYx{%
\expandafter\numonly\the\x
\edef\b{\y=\xx\y}%
\b
}%
\def\calcsin{% Find sin(\x) and put it in \y. Say \x is in degrees.
\x=0.0174533\x % Convert to radians.
\y=\x
\MULTyBYx
\xsquare=\y
\MULTyBYx
\MULTyBYx
\xfourth=\y
\y=1pt
\advance\y by -0.1666666\xsquare
\advance\y by 0.008333333\xfourth
\MULTyBYx
}%
% Example of use:
%\x=23pt \calcsin \expandafter\numonly\the\y
% Now \xx should contain the sine of 23 degrees.
%\def\sine#1{\x=#1 \calcsin \expandafter\numonly\the\y \message{sine of
%#1 is \xx}}
%----------------------------------------------------------
% given a box with width W and height H, then its height after rotation by R
% is W * sin(R) + H * cos(R), and it extends W * cos(R) to the right
% and H * sin(R) to the left
% (arithmetic courtesy of Nico Poppelier)
%
\newdimen\xh\newdimen\xw\newdimen\xtemp\newdimen\xcos\newdimen\xsin
\newdimen\xleft\newdimen\xright
\def\MULTxtempBYxcos{\expandafter\numonly\the\xcos\edef\b{\xtemp=\xx\xtemp}\b}%
\def\MULTxtempBYxsin{\expandafter\numonly\the\xsin\edef\b{\xtemp=\xx\xtemp}\b}%