Grafici con Tikz numero 13 (funzioni)

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Prima di ogni figura ricordare di mettere

\documentclass[usenames,dvipsnames]{article}
\usepackage{pgfplots}

Prima figura

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codice prima figura

\begin{tikzpicture}
\def\centerarc[#1](#2)(#3:#4:#5) % Syntax: [draw options] (center) (initial angle:final angle:radius)
{ \draw[#1] ($(#2)+({#5*cos(#3)},{#5*sin(#3)})$) arc (#3:#4:#5); }
% Macro \centerarc presa da https://tex.stackexchange.com/a/66220
% Richiede \usetikzlibrary{calc}
\begin{axis}[
disabledatascaling,
axis equal image,
scale=0.70,
axis x line=none,
axis y line=none,
xmin = -0.7,
xmax = 0.7,
ymin = -0.7,
ymax = 0.7,
]
\draw[ultra thick,color=CornflowerBlue] (axis cs:0,0) circle[radius=1/sqrt(3)];
\addplot[no marks,very thick,SeaGreen] coordinates {(-0.289,-0.167) (0.289,0.167)};
\addplot[no marks,very thick,samples=10] coordinates {(-1/sqrt(3),0) (1/2/sqrt(3),-1/2) (1/2/sqrt(3),1/2) (-1/sqrt(3),0)} \closedcycle;
\addplot[no marks,very thick,samples=10,RubineRed] coordinates {(-0.408,-0.408) (0.408,0.408)};
\addplot[no marks,thick,samples=10,dashed,RubineRed] coordinates {(-1,-1) (1,1)};
% \addplot[mark=*,samples=10,mark size=1.5pt] coordinates {(-0.408,-0.408) (0.408,0.408)};
\addplot[no marks,very thick,samples=10,mark size=1.5pt] coordinates {(0,0) (1/2/sqrt(3),-1/2)};
\addplot[no marks,thick,dotted] coordinates {(0,0) (1/sqrt(3),0)};
\addplot[mark=*,mark size=1.5pt] coordinates {(0,0)} node[above left] {$O$};
\addplot[mark=*,mark size=1.5pt] coordinates {(-1/sqrt(3),0)} node[left] {$A$};
\addplot[mark=*,mark size=1.5pt] coordinates {(1/2/sqrt(3),-1/2)} node[below right] {$B$};
\addplot[mark=*,mark size=1.5pt] coordinates {(1/2/sqrt(3),1/2)} node[above right] {$C$};
\addplot[mark=*,mark size=1.5pt] coordinates {(1/2/sqrt(3),0)} node[below right] {$D$};
\addplot[mark=*,mark size=1.5pt,RubineRed] coordinates {(0.289,0.289)} node[right] {$P\rule{0pt}{10pt}$};
\addplot[mark=*,mark size=1.5pt,RubineRed] coordinates {(-0.211,-0.211)} node[below] {$Q\rule{0pt}{10pt}$};
\addplot[no marks] coordinates {(0.20,0.145)} node[below] {$\vartheta$};
\addplot[no marks] coordinates {(-0.144,0.25)} node[above left] {1};
\centerarc[thick](0,0)(0:45:0.11);
\centerarc[thick](0,0)(0:45:0.13);
\centerarc[thick]({1/2/sqrt(3)},-1/2)(90:120:0.13);
\centerarc[thick]({1/2/sqrt(3)},-1/2)(120:150:0.11);
\end{axis}
\end{tikzpicture}

seconda figura

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codice seconda figura

\begin{tikzpicture}
\begin{axis}[
axis equal image,
disabledatascaling,
width=0.75\textwidth,
axis x line=none,
axis y line=none,
axis on top,
xmin = -0.5,
xmax = 3.5,
ymin = -0.3,
ymax = 1.5
]
\addplot[very thick,samples=10,no marks,fill=Apricot!30] coordinates {(0,0) (1,0) (0,1.272) (0,0)} \closedcycle;
\addplot[very thick,samples=10,no marks,fill=Magenta!30] coordinates {(2,0) (3,0) (2,0.786) (2,0)} \closedcycle;
\addplot[no marks,thick] coordinates {(0,0.1) (0.1,0.1) (0.1,0)};
\addplot[no marks,thick] coordinates {(2,0.1) (2.1,0.1) (2.1,0)};
\centerarc[thick](0,1.272)(-90:-52:0.2);
\centerarc[thick](2,0.786)(-90:-35:0.15);
\addplot[no marks] coordinates {(0,1.272)} node[above left] {$A$};
\addplot[no marks] coordinates {(0,0)} node[below left] {$B$};
\addplot[no marks] coordinates {(1,0)} node[below right] {$C$};
\addplot[no marks] coordinates {(2,0.786)} node[above left] {$A$};
\addplot[no marks] coordinates {(2,0)} node[below left] {$B$};
\addplot[no marks] coordinates {(3,0)} node[below right] {$C$};
\end{axis}
\end{tikzpicture}

terza figura

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codice terza figura

\begin{tikzpicture}
\begin{axis}[
width=0.66\textwidth,
height=0.4\textwidth,
axis x line=center,
axis y line=center,
axis on top,
xmin = -0.25,
xmax = 2.9,
ymin = -0.5,
ymax = 2.9,
xlabel = {$b$},
ylabel = {$a$},
extra x ticks = {0},
extra x tick label = {$\hspace{-0.45cm}\phantom{/}O\phantom{/}$},
]
\addplot[very thick,samples=100,DarkOrchid,domain=0:2.5] {x^2};
\addplot[very thick,samples=100,SeaGreen,domain=0:2.5] {2^(-x)};
\addplot[mark=*,thick,mark options={fill=BurntOrange},mark size=3pt,draw=none] coordinates {(0.767,0.588)};
\addplot[no marks] coordinates {(1,2)} node[right] {$\color{DarkOrchid} b^2$};
\addplot[no marks] coordinates {(2,0.6)} node[right] {$\color{SeaGreen} 2^{-b}$};
\end{axis}
\end{tikzpicture}

quarta figura

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codice quarta figura

\begin{tikzpicture}
\begin{axis}[
axis equal image,
scale=0.65,
axis x line=center,
axis y line=center,
xmin = -3.5,
xmax = 3.5,
ymin = -3.9,
ymax = 3.9,
xlabel = {$x$},
ylabel = {$y$},
xtick = {-pi,-pi/2,pi/2,pi},
xticklabels = {$\phantom{/}-$$\pi\phantom{/}$, $-$$\pi/2$,$\pi/2$, $\phantom{/}\pi\phantom{/}$},
extra x ticks = {0},
extra x tick label = {$\hspace{0.45cm}O$},
colormap={yellowpurple}{rgb255(0cm)=(240, 225, 48); rgb255(1cm)=(204, 204, 255)}
]
\addplot[very thick,samples=100,mesh,point meta=x,domain=-3.5:-1.6] {1/cos(deg(x))-1};
\addplot[very thick,samples=100,mesh,point meta=x,domain=-1.53:1.53] {1/cos(deg(x))-1};
\addplot[very thick,samples=100,mesh,point meta=x,domain=1.6:3.5] {1/cos(deg(x))-1};
\addplot[no marks] coordinates {(pi/3,-3)} node {\fbox{e}};
\end{axis}
\end{tikzpicture}

quinta figura

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codice quinta figura

\begin{tikzpicture}
\begin{axis}[
width=0.75\textwidth,
height=0.5\textwidth,
axis x line=center,
axis y line=center,
axis on top,
xmin = -pi/6,
xmax = 7.5,
ymin = -1.4,
ymax = 1.4,
xlabel = {$x$},
ylabel = {$y$},
xtick = {pi/2,pi,3*pi/2,2*pi},
xticklabels = {$\pi/2$, $\phantom{/}\pi\phantom{/}$, $3\pi/2$, $\phantom{/}2\pi\phantom{/}$},
extra x ticks = {0},
extra x tick label = {$\hspace{-0.45cm}\phantom{/}O\phantom{/}$},
x tick label style={above},
domain=-pi:2.5*pi
]

\path[name path=below] (axis cs:0,-2) -- (axis cs:2*pi,-2);
\path[name path=above] (axis cs:0,+2) -- (axis cs:2*pi,2);
\addplot[Gray!10] fill between[of = below and above, soft clip={domain=0:2*pi}];
\addplot[very thick,samples=100,Emerald] {sin(deg(x))^3};
\addplot[very thick,samples=100,BurntOrange] {-cos(deg(x))^2};
\addplot[no marks,dashed] coordinates {(2*pi,-5) (2*pi,5)};
\addplot[mark=*,Purple,mark size=3pt,draw=none] coordinates {(3.997,-0.43) (5.428,-0.43)};
\addplot[no marks] coordinates {(2.1,1)} node[right] {$\color{Emerald} \sin^3(x)$};
\addplot[no marks] coordinates {(0.3,-1)} node[right] {$\color{BurntOrange} -\cos^2(x)$};
\end{axis}
\end{tikzpicture}