Grafici con Tikz numero 16 (funzioni)

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Prima di ogni figura ricordare di mettere

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

Prima figura

Rendered by QuickLaTeX.com

codice prima figura

\begin{tikzpicture}
\begin{axis}[
disabledatascaling,
axis equal image,
axis x line=center,
axis y line=center,
scale=0.9,
xmin = -2.5,
xmax = 2.5,
ymin = -1.3,
ymax = 1.7,
xlabel = {$\cos(\vartheta)$},
ylabel = {$\sin(\vartheta)$},
xtick = \empty,
ytick = \empty,
extra x ticks = {0},
extra x tick label = {$\hspace{0.6cm}O$},
]

\draw[thick] (axis cs:1,0) arc [radius=1,start angle=0,end angle=360];

\addplot[no marks] coordinates {(sqrt(3)/2,1/2) (-sqrt(3)/2,-1/2)};
\addplot[no marks] coordinates {(-0.786,0.618) (0,0) (0.643,0.766)};

\draw[stealth-stealth,ultra thick,BurntOrange] (axis cs:1,0) arc [radius=1,start angle=0,end angle=30] node[below right] {$\ A$};
\draw[stealth-stealth,ultra thick,Bittersweet] (axis cs:0.643,0.766) arc [radius=1,start angle=50,end angle=90] node[pos=0.5,above] {$\ \ B$};
\draw[stealth-stealth,ultra thick,ForestGreen] (axis cs:0,1) arc [radius=1,start angle=90,end angle=141.83] node[label={[shift={(0.2,0.1)}]$C$}] {};
\draw[stealth-stealth,ultra thick,Aquamarine] (axis cs:-1,0) arc [radius=1,start angle=180,end angle=210] node[label={[shift={(-0.35,-0.05)}]$D$}] {};
\draw[stealth-stealth,ultra thick,Thistle] (axis cs:0,-1) arc [radius=1,start angle=270,end angle=360] node[label={[shift={(-0.1,-1.1)}]$E$}] {};

\end{axis}
\end{tikzpicture}

seconda figura

Rendered by QuickLaTeX.com

codice seconda figura

\begin{tikzpicture}
\begin{axis}[
axis on top,
disabledatascaling,
axis equal image,
axis x line=center,
axis y line=center,
scale=1.5,
xmin = -2.5,
xmax = 2.5,
ymin = -1.4,
ymax = 2.0,
xlabel = {$\cos(\vartheta)$},
ylabel = {$\sin(\vartheta)$},
xtick = \empty,
ytick = \empty,
extra x ticks = {0},
extra x tick label = {$\hspace{0.6cm}O$},
]

\draw[very thick] (axis cs:1,0) arc [radius=1,start angle=0,end angle=360];
\addplot[very thick,name path=parabola_neg,samples=100,domain=-2.5:0,NavyBlue] {x^2};
\addplot[very thick,name path=parabola_pos,samples=100,domain=0:2.5,NavyBlue] {x^2};
\addplot[very thick,name path=bisettrice,BurntOrange] {x};
\addplot[very thick,name path=basso,domain=0:2.5,draw=none] {-2};
\addplot[very thick,name path=alto_neg,domain=-2.5:0,draw=none] {3};
\addplot[very thick,name path=alto,domain=-2.5:2.5,draw=none] {3};

\addplot[ProcessBlue!20] fill between[of=basso and parabola_pos, soft clip={domain=0:2.5}];
\addplot[ProcessBlue!20] fill between[of=parabola_neg and alto_neg, soft clip={domain=-2.5:0}];
\addplot[pattern=north west lines,pattern color=Dandelion] fill between[of=bisettrice and alto, soft clip={domain=-2.5:2.5}];

\addplot[mark=none,BurntOrange] coordinates {(-0.85,-1.1)} node[rotate=45] {$y=x$};
\addplot[mark=none,NavyBlue] coordinates {(-1.4,1.3)} node[rotate=-66] {$y=x^2$};

\addplot[mark=*,Gray] coordinates {(1,1)} node[right] {\raisebox{-3ex}{$(1,1)$}};

\draw[stealth-stealth,ultra thick,Gray] (axis cs:1,0) arc [radius=1,start angle=0,end angle=30] node[below right] {$\ A$};
\draw[stealth-stealth,ultra thick,Gray] (axis cs:0.643,0.766) arc [radius=1,start angle=50,end angle=90] node[pos=0.5,above] {$\ \ B$};
\draw[stealth-stealth,ultra thick,ForestGreen] (axis cs:0,1) arc [radius=1,start angle=90,end angle=141.83] node[label={[shift={(0.2,0.1)}]$C$}] {};
\draw[stealth-stealth,ultra thick,Gray] (axis cs:-1,0) arc [radius=1,start angle=180,end angle=210] node[label={[shift={(-0.35,-0.05)}]$D$}] {};
\draw[stealth-stealth,ultra thick,Gray] (axis cs:0,-1) arc [radius=1,start angle=270,end angle=360] node[label={[shift={(-0.1,-1.1)}]$E$}] {};

\end{axis}
\end{tikzpicture}

terza figura

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codice terza figura

\begin{tikzpicture}
\begin{axis}[
axis on top,
disabledatascaling,
axis equal image,
axis x line=center,
axis y line=center,
xmin = -5.9,
xmax = 3.9,
ymin = -2.9,
ymax = 2.9,
xlabel = {$x$},
ylabel = {$y$},
extra x ticks = {0},
extra x tick label = {$\hspace{1cm}O$},
xticklabel style={below,yshift={0.5ex},xshift={-2ex}},
xtick={-2,2},ytick={-2,2},
yticklabel style={xshift=0.5ex,yshift={1.5ex}}
]

\addplot[very thick,name path=asse,domain=-2:2,samples=100,draw=none] {0};
\addplot[very thick,name path=cerchio_sopra,domain=-2:2,samples=150] {sqrt(4-x^2)};
\addplot[very thick,name path=cerchio_sotto,domain=-2:2,samples=150] {-sqrt(4-x^2)};
\addplot[very thick,name path=linea,samples=10,blue,domain=-10:5] {1+tan(15)*(x+1)};
\addplot[very thick,samples=10,blue] {1.183-1/tan(15)*(x+0.317)};
\addplot[Yellow!20] fill between[of=cerchio_sotto and asse, soft clip={domain=-2:2}];
\addplot[Yellow!20] fill between[of=asse and linea, soft clip={domain=-1.844:1.21}];
\addplot[Yellow!20] fill between[of=asse and cerchio_sopra, soft clip={domain=-2:-1.844}];
\addplot[Yellow!20] fill between[of=asse and cerchio_sopra, soft clip={domain=1.21:2}];

\addplot[thick] coordinates {(-0.242,0.9031) (-0.52,0.8287) (-0.595,1.1087)};
\centerarc[thick](-4.7124,0)(0:15:1);
\draw[-stealth,thick](axis cs:-4.2,0.5)--(axis cs:-3.8,0.03);
\addplot[mark=none] coordinates {(-4.3,0.7)} node {$\vartheta$};

\addplot[mark=*] coordinates {(-1.844,0.774)} node[above left] {$Q$};
\addplot[mark=*] coordinates {(1.21,1.592)} node[above] {\raisebox{1ex}{$R$}};
\addplot[mark=*] coordinates {(-1,1)} node[below] {\raisebox{-2ex}{$P$\phantom{..}}};
\addplot[mark=*] coordinates {(-0.317,1.183)} node[above left] {$H$};
\addplot[mark=*] coordinates {(0.518,-1.932)} node[below right] {$\phantom{i}K$};
\addplot[mark=*] coordinates {(0,0)};
\addplot[no marks, very thick] coordinates {(0.518,-1.932) (-1,1)};
\addplot[no marks,blue] coordinates {(3,2.4)} node {$r$};

\end{axis}
\end{tikzpicture}