Tableau de signe d'une inégalité trigonométriques avec tikz
📅 December 24, 2024 | 👁️ Views: 293
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\documentclass{standalone}
\standaloneconfig{margin=1cm}
\usepackage{fontspec}
\usepackage{tikz,tkz-tab}
\usepackage{xcolor}
\usepackage{amsmath, amsfonts, amssymb, amsthm}
\usetikzlibrary{calc}
\usetikzlibrary{shapes,decorations.text, intersections}
\definecolor{RoyalBlue}{HTML}{4169E1} % Royal Blue
\definecolor{ocre}{RGB}{243,102,25} % orange color
\definecolor{DarkGreen}{HTML}{006400} % Dark Green
\everymath{\displaystyle}
\begin{document}
\begin{tikzpicture}
\node at (0,0) {
\begin{tikzpicture}
\tkzTabInit[lgt=4, espcl=2.5] %
{$x$ /1.75, $1+\tan x$ /1, $\sin 2x$ /1, $\frac{1+\tan x}{\sin 2x}$/1.75}
{$-\pi$,$\frac{-\pi}{2}$,$\frac{-\pi}{4}$,$0$,$\frac{\pi}{2}$,$\frac{3\pi}{4}$,$\pi$}
\tkzTabLine{ , +, d, -, z, +, t, +, d, -, z, +}
\tkzTabLine{z, -, t, -, t, -, z, +, t, +, t, +,z}
\tkzTabLine{d, -, d, +, z, -, z, +, d, -, z, +,d}
\end{tikzpicture}
};
\node[align=left,text width=10cm] at (2.5,7) {
~$ x\in]-\pi,\pi]\quad \frac{1+\tan x}{\sin(2x)}\ge0$
};
\node[align=left,text width=10cm] at (2.5,5) {
~$ S=\left]\frac{-\pi}{2},\frac{-\pi}{4}\right]\cup\left[0,\frac{\pi}{2}\right]\cup\left[\frac{3\pi}{4},\pi\right[$
};
\node at (7.5,5.5) {
\begin{tikzpicture}
\coordinate (A) at (0,0);
\draw[red!50] (A) circle (1.9cm);
% Draw the inner circle
\draw[red!50] (A) circle (1.4cm);
% Draw the curved line
\draw[red!50, decorate, decoration={text along path,
text={|\fontspec{DejaVu Sans}\color{red!75}\bfseries|★MOSAID RADOUAN★},
text align={align=center}, raise=-3pt}] (A) ++ (180:1.6cm) arc (180:0:1.6cm);
\draw[decorate, decoration={text along path,
text={|\fontspec{DejaVu Sans}\color{red!75}\bfseries|∞★~mosaid.xyz~★∞ },
text align={align=center}, raise=-6.5pt}] (A) ++ (180:1.53cm) arc (-180:0:1.53cm);
\node[red!75,font=\fontsize{48}{48}\fontspec{DejaVu Sans}\bfseries\selectfont] at (A) {✷};
\end{tikzpicture}
};
\node at (-6.5,5.5) {
\begin{tikzpicture}
\def\radius{1.5} %
\coordinate (O) at (0,0);
\coordinate (I) at (\radius,0);
\coordinate (M) at (-45:\radius);
\coordinate (M') at (135:\radius);
\node[above left ] at (O) {$O$};
\node[above right] at (I) {$I$};
\fill (O) circle (1.5pt);
\draw (O) circle (\radius);
\draw[] (-1.2*\radius,0) -- (1.2*\radius,0);
\draw[] (0,-1.2*\radius) -- (0,1.2*\radius);
\draw[DarkGreen, line width=0.3mm, name path = tangente] (\radius,-2) -- (\radius,2.5) ;
\foreach \x in {-3,-2.9 , ...,0.5} {
\draw[RoyalBlue, thick] (\radius-0.1,\x+\radius) -- ++(0.2,0); %
}
\draw[thick] (\radius-0.1,\radius) -- ++(0.2,0) node[right] {$1$}; %
\path [name path=OM] (O) -- ($(O)!3.5!(M)$);
\path [name intersections={of=OM and tangente, by=T}];
\fill (M) circle (1.5pt);
\fill (M') circle (1.5pt);
\fill (T) circle (1.5pt);
\draw[RoyalBlue, line width=0.5mm] ($(M)!1.2!(M')$) -- (M);
\draw[RoyalBlue, line width=0.5mm, dashed] (M') -- ($(M')!1.2!(T)$);
\node[above, font=\small, yshift=0.1cm] at (M) {$M$};
\node[below, font=\tiny] at (M) {$\frac{-\pi}{4}$};
\node[below, font=\small,yshift=-0.2cm] at (M') {$M'$};
\node[above, font=\tiny] at (M') {$\frac{3\pi}{4}$};
\draw[red, line width=0.7mm] (M) arc(-45:90:\radius);
\draw[red, line width=0.7mm] (M') arc(135:270:\radius);
\node[above, font=\small] at (90:1.2*\radius) {$\frac{\pi}{2}$};
\node[above left, font=\small] at (90:\radius) {$J$};
\node[below left, font=\small] at (-90:\radius) {$J'$};
\node[below, font=\small] at (-90:1.2*\radius) {$\frac{-\pi}{2}$};
\node[below left, font=\small] at (-\radius,0) {$-\pi$};
\node[above left, font=\small] at (-\radius,0) {$\pi$};
\node[right, font=\tiny] at (T) {$-1$};
\end{tikzpicture}\\
};
\end{tikzpicture}
\end{document}
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Frequently Asked Questions
What will I learn by the end of this course?
You will gain a solid understanding of Tableau de variations avec Tikz and be able to apply it in exams and real‑world problems.
What topics are covered in this course?
The course "Tableau de variations avec Tikz" covers key concepts of latex for figures. Designed to help students master the curriculum.
Is this course suitable for beginners?
Yes, the material is structured to be accessible while providing depth for advanced learners.
Are there exercises or practice problems?
Exercises are included to help you practice.
Does this course include solutions?
Solutions are available separately.
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