graphs of the famous sinc function and its "other side" (im sorry i can never rember those quirky option names in pgfplots- 💀)

two-sides.tex

\documentclass{article}
\usepackage[a4paper]{geometry}
\usepackage{amsmath}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}
\usetikzlibrary{calc}

\begin{document}
\begin{center}
\begin{tikzpicture}
  % Stretch factors (xscale and yscale seem to distort line width)
  \pgfmathsetmacro\xs{0.25}
  \pgfmathsetmacro\ys{1.5}
  \def\ticklen{0.35ex}
  \draw[semithick,->] (-6.5*pi*\xs,0) -- (6.5*pi*\xs,0) node[above] {$x$};
  \draw[semithick,->] (0,-0.25*\ys) -- (0,1.25*\ys) node[left] {$y$};
  \foreach \x in {2,3,...,6,-2,-3,...,-6} {
    \draw (\x*pi*\xs,\ticklen) -- (\x*pi*\xs,-\ticklen)
      node[below, font=\scriptsize] {\mathstrut$\x\pi$};
  }
  \foreach \x/\xx in {-pi/$-\pi$, pi/$\pi$} {
    \draw (\x*\xs,\ticklen) -- (\x*\xs,-\ticklen)
      node[below, font=\scriptsize] {\mathstrut\xx};
  }
  \foreach \y in {1,0.5} {
    \draw (\ticklen,\y*\ys) -- (-\ticklen,\y*\ys)
      node[left, font=\scriptsize] {\mathstrut$\y$};
  }
  % https://tex.stackexchange.com/a/128166
  \begin{axis}[
    anchor=origin,  % Align the origins
    x=1cm, y=1cm,   % Set the same unit vectors
    hide axis,
  ]
    \addplot [semithick,red,samples=1000,domain=-6.3*pi*\xs:6.3*pi*\xs]
      {\ys*sin(deg(x/\xs))/(x/\xs)};
  \end{axis}
  \node[red,right] at (pi*\xs,0.5*\ys) {$y = \dfrac{\sin(x)}{x}$};
\end{tikzpicture}
\end{center}

\begin{center}
\begin{tikzpicture}
  \pgfmathsetmacro\xs{30}
  \pgfmathsetmacro\ys{20}
  \def\ticklen{0.35ex}
  \draw[semithick,->] ({-1/(1.75*pi)*\xs},0) -- ({1/(1.75*pi)*\xs},0)
    node[above] (x) {$x$};
  \draw[semithick,->] (0,-0.1*\ys) -- (0,0.1*\ys)
    node[left] (y) {$y$};
  \begin{axis}[
    anchor=origin,  % Align the origins
    x=1cm, y=1cm,   % Set the same unit vectors
    hide axis,
  ]
    \foreach \lo/\hi/\sam in {{-1/(1.75*pi)*\xs}/{-1/(4*pi)*\xs}/500,
                              {1/(4*pi)*\xs}/{1/(1.75*pi)*\xs}/500,
                              {-1/(4*pi)*\xs}/0.0001/5000,
                              0.0001/{1/(4*pi)*\xs}/5000}
    {
      \addplot [semithick,smooth,blue,samples=\sam,domain=\lo:\hi]
        {\ys*(x/\xs)*sin(deg(1/x*\xs))};
    }
  \end{axis}
  \pgfmathsetmacro\M{1/(2*pi)}
  \draw[dashed] (-\M*\xs,-\M*\ys) -- (+\M*\xs,+\M*\ys);
  \draw[dashed] (-\M*\xs,+\M*\ys) -- (+\M*\xs,-\M*\ys);
  \foreach \x/\xsi/\xsj in {-2/-1/2\pi,-3/-1/3\pi,-4/-1/4\pi,-5/-1/5\pi,
                            2/1/2\pi,3/1/3\pi,4/1/4\pi,5/1/5\pi} {
    \path ({1/pi/(\x)*\xs},\ticklen) -- ({1/pi/(\x)*\xs},-\ticklen)
      node[below, font=\scriptsize, fill=white,
           inner sep=0.5*\ticklen] {\mathstrut$\frac\xsi\xsj$};
  }
  \node[blue,right] at (0.0075*\xs,0.11*\ys)
    {$y = x \sin\biggl(\dfrac{1}{x}\biggr)$};
\end{tikzpicture}
\end{center}
\end{document}