Tikz – esempio 16

Benvenuti nel nostro esempio 16 di utilizzo del pacchetto Tikz, una risorsa utilissima del linguaggio per comporre immagini di altissima qualità. In questo articolo proponiamo un esempio di utilizzo. Segnaliamo anche il precedente Tikz – esempio 15 e il successivo Tikz – esempio 17 per ulteriore materiale.

Buona lettura!

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

Prima figura

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

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

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}

Risorse didattiche aggiuntive per approfondire la matematica