Source Latex
\documentclass[12pt]{article}
\usepackage{amsfonts}\usepackage{amssymb}
\usepackage[french]{babel}
\usepackage{amsmath}
\usepackage[utf8]{inputenc}
\usepackage{enumerate}
\usepackage{color}
\usepackage{calc}
\usepackage{pst-plot,pst-text,pst-tree}
\usepackage{hyperref}
\hypersetup{
pdfauthor={Yoann Morel},
pdfsubject={Formulaire de mathématiques: trigonométrie},
pdftitle={Formulaire de trigonométrie},
pdfkeywords={Mathématiques, 1S, première, S,
trigoométrie, cercle trigonométrique, sinus, cosinus}
}
\hypersetup{
colorlinks = true,
linkcolor = red,
anchorcolor = red,
citecolor = blue,
filecolor = red,
urlcolor = red
}
\voffset=-1cm
% Raccourcis diverses:
\newcommand{\nwc}{\newcommand}
\nwc{\dsp}{\displaystyle}
\nwc{\ct}{\centerline}
\nwc{\bge}{\begin{equation}}\nwc{\ene}{\end{equation}}
\nwc{\bgar}{\begin{array}}\nwc{\enar}{\end{array}}
\nwc{\bgit}{\begin{itemize}}\nwc{\enit}{\end{itemize}}
\nwc{\bgen}{\begin{enumerate}}\nwc{\enen}{\end{enumerate}}
\nwc{\la}{\left\{}\nwc{\ra}{\right\}}
\nwc{\lp}{\left(}\nwc{\rp}{\right)}
\nwc{\lb}{\left[}\nwc{\rb}{\right]}
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\nwc{\vspd}{\vspace{0.2cm}}
\nwc{\vspt}{\vspace{0.3cm}}
\nwc{\vspq}{\vspace{0.4cm}}
\def\N{{\rm I\kern-.1567em N}} % Doppel-N
\def\D{{\rm I\kern-.1567em D}} % Doppel-N
\def\No{\N_0} % Doppel-N unten 0
\def\R{{\rm I\kern-.1567em R}} % Doppel R
\def\C{{\rm C\kern-4.7pt % Doppel C
\vrule height 7.7pt width 0.4pt depth -0.5pt \phantom {.}}}
\def\Q{\mathbb{Q}}
\def\Z{{\sf Z\kern-4.5pt Z}} % Doppel Z
\def\euro{\mbox{\raisebox{.25ex}{{\it =}}\hspace{-.5em}{\sf C}}}
\nwc{\tm}{\times}
\nwc{\ul}[1]{\underline{#1}}
\nwc{\scp}[1]{\scriptstyle#1}
\nwc{\scpp}[1]{\scriptscriptstyle#1}
\newcounter{nex}%[section]
\setcounter{nex}{0}
\newenvironment{EX}{%
\stepcounter{nex}\vspace{-0.2cm}
\medskip{\noindent\ul{{\bf Ex }\arabic{nex}.}}\hspace{0.1cm}
}{}
\nwc{\bgex}{\begin{EX}}\nwc{\enex}{\end{EX}}
\nwc{\bgmp}{\begin{minipage}}\nwc{\enmp}{\end{minipage}}
\headheight=0cm
\textheight=26.4cm
\topmargin=-1.8cm
\footskip=1.cm
\textwidth=19.5cm
\oddsidemargin=-1.5cm
\setlength{\unitlength}{1cm}
\renewcommand{\thesection}{\Roman{section}}
\renewcommand{\thesubsection}{\arabic{subsection}}
\nwc{\deftitle}{Définition}
\newlength{\ldef}\settowidth{\ldef}{\deftitle:}
\nwc{\bgdef}[1]{\paragraph{\ul{\deftitle:}}
\begin{minipage}[t]{\textwidth-\ldef-1em}{\it #1}
\end{minipage}
}
\nwc{\defstitle}{Définitions}
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\begin{minipage}[t]{\textwidth-\ldefs+1.5em}{\it #1}
\end{minipage}
}
\nwc{\proptitle}{Propriété}
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\nwc{\bgprop}[1]{\paragraph{\ul{\proptitle:}}
\begin{minipage}[t]{\textwidth-\lprop-1em}{\it #1}
\end{minipage}
}
\nwc{\coroltitle}{Corollaire}
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\nwc{\bgcorol}[1]{\paragraph{\ul{\coroltitle:}}
\begin{minipage}[t]{\textwidth-\lprop-2em}{\it #1}
\end{minipage}
}
\usepackage{fancyhdr}
%\usepackage{lastpage}
\pagestyle{fancyplain}
\setlength{\headheight}{0cm}
\renewcommand{\headrulewidth}{0pt}
\renewcommand{\footrulewidth}{0.1pt}
\lhead{}\chead{}\rhead{}
\lfoot{Y. Morel - \url{xymaths.free.fr/Lycee/1S/}}
\cfoot{}%
\rfoot{Probablilités - $1^{\mbox{\scriptsize{ère}}}S$ - \thepage/\pageref{LastPage}}
\footskip=0.7cm
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
\vspace*{.2cm}
\ct{\Large\textbf{Formulaire de trigonométrie}}
\vspace{1cm}
\paragraph{Valeurs remarquables des fonctions trigonométriques.}
\ \vspq
\bgmp{10cm}
\psset{unit=3cm}%{xunit=5cm,yunit=5cm}
\begin{pspicture}(-1,-1.45)(1.5,1.5)
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\psline[linewidth=0.8pt](0,0)(0.707,0.707)
\psline[linewidth=0.8pt](0,0)(0.5,0.866)
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\put(0.5,1){$\dsp\frac{\pi}{3}$}
\put(0.75,0.8){$\dsp\frac{\pi}{4}$}
\put(0.95,0.5){$\dsp\frac{\pi}{6}$}
\put(-0.05,1.15){$\dsp\frac{\pi}{2}$}
\put(-1.15,-0.02){$\pi$}
\put(-0.1,-1.2){$\dsp\frac{3\pi}{2}$}
\end{pspicture}
\enmp
\bgmp{6cm}
\begin{tabular}{|c|c|c|c|c|c|}\hline
\raisebox{0.1cm}[1.cm][0.5cm]{$x$} & \ \ $0$\ \ & $\dsp\frac{\pi}{6}$ &
$\dsp\frac{\pi}{4}$ & $\dsp\frac{\pi}{3}$ & $\dsp\frac{\pi}{2}$
\\\hline
\raisebox{0.1cm}[1.cm][0.5cm]{$\dsp\sin$} & $0$ & $\dsp\frac{1}{2}$ &
$\dsp\frac{\sqrt{2}}{2}$ & $\dsp\frac{\sqrt{3}}{2}$ & $1$
\\\hline
\raisebox{0.1cm}[1.cm][0.5cm]{$\dsp\cos$} & $1$ &
$\dsp\frac{\sqrt{3}}{2}$ & $\dsp\frac{\sqrt{2}}{2}$ &
$\dsp\frac{1}{2}$ & $0$
\\\hline
\raisebox{0.1cm}[1.cm][0.5cm]{$\dsp\tan$} & $0$ &
$\dsp\frac{\sqrt{3}}{3}$ & $1$ & $\sqrt{3}$ &$+\infty$
\\\hline
\end{tabular}
\enmp
\vspace{1cm}\hspace{-1.3cm}
\bgmp{10cm}
\psset{unit=3cm}%{xunit=5cm,yunit=5cm}
\begin{pspicture}(-1.5,1.5)(1.5,1.5)
\pscircle(0,0){1}
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\psarc[linewidth=0.6pt]{->}(0,0){0.4}{0}{19}
\put(0.45,0.05){\large{$x$}}
\psline[linewidth=0.8pt](-1.2,-0.4)(1.2,.4)
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\put(1.25,-.03){\large{$0$}}
\put(1.25,0.4){\large{$x$}}
\put(1.2,-0.45){\large{$-x$}}
\put(-1.5,0.4){\large{$\pi-x$}}
\put(-1.5,-0.45){\large{$\pi+x$}}
\put(-1.4,0.){\large{$\pi$}}
\put(-0.7,1.25){\large{$\dsp\frac{\pi}{2}+x$}}
\put(0.25,1.25){\large{$\dsp\frac{\pi}{2}-x$}}
\put(-.05,1.35){\large{$\dsp\frac{\pi}{2}$}}
\put(-0.75,-1.3){\large{$\dsp\frac{3\pi}{2}-x$}}
\put(-0.1,-1.4){\large{$\dsp\frac{3\pi}{2}$}}
\put(0.28,-1.3){\large{$\dsp\frac{3\pi}{2}+x$}}
\put(0.7,-0.1){$\cos x$}
\put(-0.1,0.35){$\sin x$}
\end{pspicture}
\enmp
\bgmp[t]{10cm}
\paragraph{Parité des fonctions sinus et cosinus.}
\
La fonction cosinus est paire, la fonction sinus est impaire.
En d'autres termes, pour tout nombre réel $x$,
%\bgmp[b]{3cm}
\[\la\bgar{ll}
\cos(-x) = \cos x \vspd\\
\sin(-x) = -\sin x
\enar\right.
\]%\enmp
\vspt
\paragraph{Autres relations.} Pour tout nombre réel $x$,
\[
\la\bgar{ll}
\dsp \cos\lp\frac{\pi}{2}-x\rp = \sin x \vspd\\
\dsp \sin\lp\frac{\pi}{2}-x\rp = \cos x
\enar\right.
\hspace{0.6cm}
\la\bgar{ll}
\dsp \cos\lp\frac{\pi}{2}+x\rp = -\sin x \vspd\\
\dsp \sin\lp\frac{\pi}{2}+x\rp = \cos x
\enar\right.
\]
\[ \la\bgar{ll}
\cos\lp\pi-x\rp = -\cos x \vspd\\
\sin\lp\pi-x\rp = \sin x
\enar\right.
\hspace{0.6cm}
\la\bgar{ll}
\cos\lp\pi+x\rp = -\cos x \vspd\\
\sin\lp\pi+x\rp = -\sin x
\enar\right.
\]
\enmp
\label{LastPage}
\end{document}
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