% (find-LATEX "2020-2-C2-ids-trigs.tex")
% (defun c () (interactive) (find-LATEXsh "lualatex -record 2020-2-C2-ids-trigs.tex" :end))
% (defun C () (interactive) (find-LATEXsh "lualatex 2020-2-C2-ids-trigs.tex" "Success!!!"))
% (defun D () (interactive) (find-pdf-page      "~/LATEX/2020-2-C2-ids-trigs.pdf"))
% (defun d () (interactive) (find-pdftools-page "~/LATEX/2020-2-C2-ids-trigs.pdf"))
% (defun e () (interactive) (find-LATEX "2020-2-C2-ids-trigs.tex"))
% (defun l () (interactive) (find-LATEX "2020-2-C2-ids-trigs.lua"))
% (defun o () (interactive) (find-LATEX "2020-2-C2-ids-trigs.tex"))
% (defun u () (interactive) (find-latex-upload-links "2020-2-C2-ids-trigs"))
% (defun v () (interactive) (find-2a '(e) '(d)))
% (defun d0 () (interactive) (find-ebuffer "2020-2-C2-ids-trigs.pdf"))
% (defun cv () (interactive) (C) (ee-kill-this-buffer) (v) (g))
%          (code-eec-LATEX "2020-2-C2-ids-trigs")
% (find-pdf-page   "~/LATEX/2020-2-C2-ids-trigs.pdf")
% (find-sh0 "cp -v  ~/LATEX/2020-2-C2-ids-trigs.pdf /tmp/")
% (find-sh0 "cp -v  ~/LATEX/2020-2-C2-ids-trigs.pdf /tmp/pen/")
%     (find-xournalpp "/tmp/2020-2-C2-ids-trigs.pdf")
%   file:///home/edrx/LATEX/2020-2-C2-ids-trigs.pdf
%               file:///tmp/2020-2-C2-ids-trigs.pdf
%           file:///tmp/pen/2020-2-C2-ids-trigs.pdf
% http://angg.twu.net/LATEX/2020-2-C2-ids-trigs.pdf
% (find-LATEX "2019.mk")
% (find-CN-aula-links "2020-2-C2-ids-trigs" "2" "c2m202it" "c2it")
%
% Video:
% (find-ssr-links "c2m202it" "2020-2-C2-ids-trigs" "{naoexiste}}")
% (code-video     "c2m202itvideo" "$S/http/angg.twu.net/eev-videos/2020-2-C2-ids-trigs.mp4")
% (find-c2m202itvideo "0:00")

% «.defs»	(to "defs")
% «.title»	(to "title")
% «.div-polis»	(to "div-polis")
%
% «.djvuize»	(to "djvuize")

\documentclass[oneside,12pt]{article}
\usepackage[colorlinks,citecolor=DarkRed,urlcolor=DarkRed]{hyperref} % (find-es "tex" "hyperref")
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{pict2e}
\usepackage[x11names,svgnames]{xcolor} % (find-es "tex" "xcolor")
\usepackage{colorweb}                  % (find-es "tex" "colorweb")
%\usepackage{tikz}
%
% (find-dn6 "preamble6.lua" "preamble0")
%\usepackage{proof}   % For derivation trees ("%:" lines)
%\input diagxy        % For 2D diagrams ("%D" lines)
%\xyoption{curve}     % For the ".curve=" feature in 2D diagrams
%
\usepackage{edrx15}               % (find-LATEX "edrx15.sty")
\input edrxaccents.tex            % (find-LATEX "edrxaccents.tex")
\input edrxchars.tex              % (find-LATEX "edrxchars.tex")
\input edrxheadfoot.tex           % (find-LATEX "edrxheadfoot.tex")
\input edrxgac2.tex               % (find-LATEX "edrxgac2.tex")
\input 2017planar-has-defs.tex    % (find-LATEX "2017planar-has-defs.tex" "defub")
%
%\usepackage[backend=biber,
%   style=alphabetic]{biblatex}            % (find-es "tex" "biber")
%\addbibresource{catsem-slides.bib}        % (find-LATEX "catsem-slides.bib")
%
% (find-es "tex" "geometry")
\usepackage[a6paper, landscape,
            top=1.5cm, bottom=.25cm, left=1cm, right=1cm, includefoot
           ]{geometry}
%
\begin{document}

\catcode`\^^J=10
\directlua{dofile "dednat6load.lua"}  % (find-LATEX "dednat6load.lua")

%L dofile "edrxtikz.lua"  -- (find-LATEX "edrxtikz.lua")
%L dofile "edrxpict.lua"  -- (find-LATEX "edrxpict.lua")
%L dofile "2020-2-C2-ids-trigs.lua" -- (find-LATEX "2020-2-C2-ids-trigs.lua")
\pu

% «defs»  (to ".defs")
% (find-LATEX "edrx15.sty" "colors-2019")
\long\def\ColorRed   #1{{\color{Red1}#1}}
\long\def\ColorViolet#1{{\color{MagentaVioletLight}#1}}
\long\def\ColorViolet#1{{\color{Violet!50!black}#1}}
\long\def\ColorGreen #1{{\color{SpringDarkHard}#1}}
\long\def\ColorGreen #1{{\color{SpringGreenDark}#1}}
\long\def\ColorGreen #1{{\color{SpringGreen4}#1}}
\long\def\ColorGray  #1{{\color{GrayLight}#1}}
\long\def\ColorGray  #1{{\color{black!30!white}#1}}
\long\def\ColorBrown #1{{\color{Brown}#1}}
\long\def\ColorBrown #1{{\color{brown}#1}}
\long\def\ColorOrange#1{{\color{orange}#1}}

\long\def\ColorShort #1{{\color{SpringGreen4}#1}}
\long\def\ColorLong  #1{{\color{Red1}#1}}

\def\frown{\ensuremath{{=}{(}}}
\def\True {\mathbf{V}}
\def\False{\mathbf{F}}
\def\D    {\displaystyle}

\def\drafturl{http://angg.twu.net/LATEX/2020-2-C2.pdf}
\def\drafturl{http://angg.twu.net/2020.2-C2.html}
\def\draftfooter{\tiny \href{\drafturl}{\jobname{}} \ColorBrown{\shorttoday{} \hours}}



%  _____ _ _   _                               
% |_   _(_) |_| | ___   _ __   __ _  __ _  ___ 
%   | | | | __| |/ _ \ | '_ \ / _` |/ _` |/ _ \
%   | | | | |_| |  __/ | |_) | (_| | (_| |  __/
%   |_| |_|\__|_|\___| | .__/ \__,_|\__, |\___|
%                      |_|          |___/      
%
% «title»  (to ".title")
% (c2m202itp 1 "title")
% (c2m202ita   "title")

\thispagestyle{empty}

\begin{center}

\vspace*{1.2cm}

{\bf \Large Cálculo 2 - 2020.2}

\bsk

Aula ??: Identidades trigonométricas

\bsk

Eduardo Ochs - RCN/PURO/UFF

\url{http://angg.twu.net/2020.2-C2.html}

\end{center}

\newpage

% «div-polis»  (to ".div-polis")
% (c2m202itp 2 "div-polis")
% (c2m202ita   "div-polis")

Nos slides sobre Frações Parciais nós vimos que contas com

polinômios são parecidas com contas com números ``sem vai um''...



%R A = 1/ __ __ __ __ \
%R      |     2  3  1 |
%R      | !X     1  2 |
%R      |    -------- |
%R      |        1  2 |
%R      |     3  6    |
%R      |  2  4       |
%R      |  ---------- |
%R      \  2  7  7  2 /
%R
%R cc = A:toccells()
%R mp = MixedPicture.new({zdef="mult numeric", scale="14pt", meta="", celllower="3.5pt"})
%R cc:addcellsto(mp)
%R cc:addLineto(mp, {1,2}, {4,2})
%R cc:addLineto(mp, {0,5}, {4,5})
%R
%R mp:output()
%R
%R A = 1/ ____ _____  ___  __ \
%R      |       2x^2  +3x  +1 |
%R      |  !X           x  +2 |
%R      |       ------------- |
%R      |               x  +2 |
%R      |       3x^2  +6x     |
%R      | 2x^3 +4x^2          |
%R      | ------------------- |
%R      \ 2x^3 +7x^2  +7x  +2 /
%R
%R cc = A:toccells()
%R cc.xscale = 2
%R mp = MixedPicture.new({zdef="mult poly", scale="14pt", meta="", celllower="3.5pt"})
%R cc:addcellsto(mp)
%R cc:addLineto(mp, {1,2}, {4,2})
%R cc:addLineto(mp, {0,5}, {4,5})
%R
%R mp:output()

% (c2m202fpp 6 "contas-sem-vai-um")
% (c2m202fp    "contas-sem-vai-um")
% (c2m202fpp 7 "div-polis")
% (c2m202fp    "div-polis")

%R A = 1/ _ _ _ _ _   _ _ _ \
%R      |   2 7 7 3 |   1 2 |
%R      |           +------ |
%R      | - 2 4       2 3 1 |
%R      |   ---             |
%R      |     3 7           |
%R      |   - 3 6           |
%R      |     ---           |
%R      |       1 3         |
%R      |     - 1 2         |
%R      |       ---         |
%R      \         1         /
%R
%R cc = A:toccells()
%R mp = MixedPicture.new({zdef="div numeric", scale="14pt", meta=""})
%R cc:addcellsto(mp)
%R cc:addLineto(mp, {1,2}, {3,2})
%R cc:addLineto(mp, {2,4}, {4,4})
%R cc:addLineto(mp, {3,6}, {5,6})
%R cc:addLineto(mp, {5,0}, {5,1}, {8,1})
%R mp:output()
%R
%R A = 1/ _ _____ ______ ____  ___   ____ ___ ___ \
%R      |    2x^3 +7x^2  +7x   +3  |        x  +2 |
%R      |                          +------------- |
%R      | - (2x^3 +4x^2)             2x^2 +3x  +1 |
%R      |   ------------                          |
%R      |          3x^2  +7x                      |
%R      |      -  (3x^2  +6x)                     |
%R      |         -----------                     |
%R      |                  x   +3                 |
%R      |            -    (x   +2)                |
%R      |                ---------                |
%R      \                       1                 /
%R
%R cc = A:toccells()
%R cc.xscale = 2
%R mp = MixedPicture.new({zdef="div poly 1", scale="14pt", meta=""})
%R mp = MixedPicture.new({zdef="div poly 1", scale="14pt", meta="", celllower="3.5pt"})
%R cc:addcellsto(mp)
%R cc:addLineto(mp, {1,2}, {3,2})
%R cc:addLineto(mp, {2,4}, {4,4})
%R cc:addLineto(mp, {3,6}, {5,6})
%R cc:addLineto(mp, {5,0}, {5,1}, {8,1})
%R
%R mp:output()
\pu
%
$$\def\X{×}
  \def\H#1{\hspace*{#1}}
  \scalebox{0.8}{$
  \begin{array}{rcl}
  \zha{mult numeric} \H{1cm} &⇒& \H{1.75cm} \zha{mult poly}
  \\[60pt]
  \zha{div numeric}  \H{0.5cm} &⇒& \H{0cm}  \zha{div poly 1}
  \end{array}
  $}
$$



% Exemplo numa prova antiga:
% (find-pdf-page "~/LATEX/2018-2-C2-P1.pdf" 2)
% (find-LATEX "2018-2-C2-P1.tex" "gab-2")
% http://angg.twu.net/LATEX/2018-2-C2-P1.pdf


\newpage

%\printbibliography

\GenericWarning{Success:}{Success!!!}  % Used by `M-x cv'

\end{document}

%  ____  _             _         
% |  _ \(_)_   ___   _(_)_______ 
% | | | | \ \ / / | | | |_  / _ \
% | |_| | |\ V /| |_| | |/ /  __/
% |____// | \_/  \__,_|_/___\___|
%     |__/                       
%
% «djvuize»  (to ".djvuize")
% (find-LATEXgrep "grep --color -nH --null -e djvuize 2020-1*.tex")

 (eepitch-shell)
 (eepitch-kill)
 (eepitch-shell)
# (find-fline "~/2020.2-C2/")
# (find-fline "~/LATEX/2020-2-C2/")
# (find-fline "~/bin/djvuize")

cd /tmp/
for i in *.jpg; do echo f $(basename $i .jpg); done

f () { rm -fv $1.png $1.pdf; djvuize $1.pdf }
f () { rm -fv $1.png $1.pdf; djvuize WHITEBOARDOPTS="-m 1.0" $1.pdf; xpdf $1.pdf }
f () { rm -fv $1.png $1.pdf; djvuize WHITEBOARDOPTS="-m 0.5" $1.pdf; xpdf $1.pdf }
f () { rm -fv $1.png $1.pdf; djvuize WHITEBOARDOPTS="-m 0.25" $1.pdf; xpdf $1.pdf }
f () { cp -fv $1.png $1.pdf       ~/2020.2-C2/
       cp -fv        $1.pdf ~/LATEX/2020-2-C2/
       cat <<%%%
% (find-latexscan-links "C2" "$1")
%%%
}

f 20201213_area_em_funcao_de_theta
f 20201213_area_em_funcao_de_x
f 20201213_area_fatias_pizza



%  __  __       _        
% |  \/  | __ _| | _____ 
% | |\/| |/ _` | |/ / _ \
% | |  | | (_| |   <  __/
% |_|  |_|\__,_|_|\_\___|
%                        
% <make>

 (eepitch-shell)
 (eepitch-kill)
 (eepitch-shell)
# (find-LATEXfile "2019planar-has-1.mk")
make -f 2019.mk STEM=2020-2-C2-ids-trigs veryclean
make -f 2019.mk STEM=2020-2-C2-ids-trigs pdf

% Local Variables:
% coding: utf-8-unix
% ee-tla: "c2m202it"
% End:
