Prima figura
Codice prima figura
\begin{tikzpicture}
\begin{axis}[
axis equal image,
scale=1.65,
axis x line=center,
axis y line=center,
xmin = -11*pi/4-1,
xmax = 11*pi/4+1,
ymin = -11*pi/4-1,
ymax = 11*pi/4+1,
xlabel = {$x$},
ylabel = {$y$},
xtick = {-2*pi,-pi,pi,2*pi},
xticklabels = {$-2\pi$, $\phantom{2}-\pi\phantom{2}$, $\phantom{2}\pi\phantom{2}$, $2\pi$},
ytick = {-2*pi,-pi,pi,2*pi},
yticklabels = {$-2\pi$, $\phantom{2}-\pi\phantom{2}$, $\phantom{2}\pi\phantom{2}$, $2\pi$},
extra x ticks = {0},
extra x tick label = {$\hspace{0.6cm}O$},
tick label style={font=\scriptsize},
domain=-9*pi/4:9*pi/4,
% restrict y to domain=-7.854:7.854
]
\foreach \r in {2,3,...,8} {
\addplot[thick,color=red,samples=100,domain=-\r:\r] {sqrt(\r*\r-x^2)};
\addplot[thick,color=red,samples=100,domain=-\r:\r] {-sqrt(\r*\r-x^2)};
};
\foreach \r in {2,3,...,8} {
\addplot[thick,color=red,samples=100,domain=-10:-\r] {sqrt(x^2-\r*\r)};
\addplot[thick,color=red,samples=100,domain=-10:-\r] {-sqrt(x^2-\r*\r)};
\addplot[thick,color=red,samples=100,domain=\r:10] {sqrt(x^2-\r*\r)};
\addplot[thick,color=red,samples=100,domain=\r:10] {-sqrt(x^2-\r*\r)};
\addplot[thick,color=red,samples=100,domain=-10:10] {sqrt(\r*\r+x^2)};
\addplot[thick,color=red,samples=100,domain=-10:10] {-sqrt(\r*\r+x^2)};
};
\addplot[thick,color=red,samples=20,domain=-10:10] {x};
\addplot[thick,color=red,samples=20,domain=-10:10] {-x};
\end{axis}
\end{tikzpicture}
Seconda figura
Terza figura
Codice terza figura
\begin{tikzpicture}
\begin{axis}[
scale=2.5,
axis equal image,
axis x line=center,
axis y line=center,
xmin = -8.5,
xmax = 8.5,
ymin = -8.5,
ymax = 8.5,
xlabel = {$x$},
ylabel = {$y$},
extra x ticks = {0},
extra x tick label = {$\hspace{-0.9cm}0$},
y label style={anchor=north east}
]
\addplot[thin, samples=10,name path=asse,domain=-8.5:8.5] {0};
\addplot[white, thin, samples=10,name path=assedown,domain=-8.5:8.5] {-8};
\addplot[white, thin, samples=10,name path=asseup,domain=-8.5:8.5] {8};
\addplot[black, very thick, dashed, domain=(-2*sqrt(2):2*sqrt(2)),samples=400,name path=radiceup] {sqrt(-x^2+8)};
\addplot[black, very thick, dashed, domain=(-2*sqrt(2):2*sqrt(2)),samples=400,name path=radicedown] {-sqrt(-x^2+8)};
\addplot[black, very thick, dashed, domain=(-8:-3),samples=400,name path=iperbole-1] {-pi/x};
\addplot[black, very thick, dashed, domain=(-1.2:-0.3),samples=400,name path=iperbole-1a] {-pi/x};
\addplot[black, very thick, dashed, domain=(3:8),samples=400,name path=iperbole-1b] {-pi/x};
\addplot[black, very thick, dashed, domain=(0.3:1.2),samples=400,name path=iperbole-1c] {-pi/x};
\addplot[black, very thick, dashed, domain=(-8:-3),samples=400,name path=iperbole1] {pi/x};
\addplot[black, very thick, dashed, domain=(-1.2:-0.3),samples=400,name path=iperbole1a] {pi/x};
\addplot[black, very thick, dashed, domain=(3:8),samples=400,name path=iperbole1b] {pi/x};
\addplot[black, very thick, dashed, domain=(0.3:1.2),samples=200,name path=iperbole1c] {pi/x};
\addplot[black, very thick, dashed, domain=(-8:-0.1),samples=200,name path=iperbole2] {2*pi/x};
\addplot[black, very thick, dashed, domain=(-8:-0.1),samples=200,name path=iperbole-2] {-2*pi/x};
\addplot[black, very thick, dashed, domain=(-8:-0.1),samples=200,name path=iperbole-3] {-3*pi/x};
\addplot[black, very thick, dashed, domain=(-8:-0.1),samples=200,name path=iperbole3] {3*pi/x};
\addplot[black, very thick, dashed, domain=(0.1:8),samples=200,name path=iperbole2] {2*pi/x};
\addplot[black, very thick, dashed, domain=(0.1:8),samples=200,name path=iperbole-2] {-2*pi/x};
\addplot[black, very thick, dashed, domain=(0.1:8),samples=200,name path=iperbole-3] {-3*pi/x};
\addplot[black, very thick, dashed, domain=(0.1:8),samples=200,name path=iperbole3] {3*pi/x};
\addplot[pink] fill between [of=asse and assedown, soft clip={domain=-8.5:-2.828}];
\addplot[pink] fill between [of=asse and asseup, soft clip={domain=-8.5:-2.828}];
\addplot[pink] fill between [of=asse and assedown, soft clip={domain=2.828:8}];
\addplot[pink] fill between [of=asse and asseup, soft clip={domain=2.828:8}];
\addplot[pink] fill between [of=radicedown and assedown, soft clip={domain=-2.828:2.828}];
\addplot[pink] fill between [of=asseup and radiceup, soft clip={domain=-2.828:2.828}];
\end{axis}
\end{tikzpicture}