Plot a periodic function

Question

I want to create a figure representating a generic periodic function. Here is my attempt.

\documentclass[tikz,border=10pt]{standalone}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}[>=latex,scale=0.6]
    % Axe horizontal
    \draw[thick, ->] (-4,0) -- (10,0);

    % Fonction (courbe périodique)
    \draw[thick]
    plot [smooth, samples=100, domain=-3:9]
    (\x,{0.5*sin(2*\x r) + sin(3*\x r) + 0.2*sin(4*\x r)});

    % node f
    \node at (8.5,-0.5) {$f$};

    % Ligne verticale
    \draw[thick] (0,-2) -- (0,2);

    % Indication de la période p (approximative)
    \draw[<->] (0.53, 1.607) -- ({2*pi+0.53},1.607) node[midway, above] {$p$};
\end{tikzpicture}
\end{document}

Is there a better and easier way to produce a similar plot that demands less computations? Thank you very much once again!

Answer 1

I suggest little changes of @Zarko's answer, for a better (I think) visualisation of a periodic function in a book:

Code:

\documentclass[tikz, border=5pt]{standalone}
\usetikzlibrary{arrows.meta,
    quotes}

\begin{document}
    \begin{tikzpicture}[scale=0.5, 
        >=Stealth,%Latex,
        trig format=rad, % or deg   <------
        samples=201         ]
        % Axes
        \draw[->] (-1.1*pi,0) -- ++ (5.3*pi,0) node[below left] {$f$};
        \draw[->] (0,-2)      -- ++ (0,5)    node[below left] {$A$};
        % Fonction (courbe périodique)
        \draw[thick]    plot [domain=-pi:4*pi]
        (\x,{0.5*sin(2*\x) + sin(3*\x) + 0.2*sin(4*\x)});
        \draw[thick,red]    plot [domain=0:2*pi]
        (\x,{0.5*sin(2*\x) + sin(3*\x) + 0.2*sin(4*\x)});
        % Indication de la période p 
        \draw[|<->|] (0, 2) to ["$p=2\pi$"]   ++ (2*pi,0);
        \draw[|<->|] (2*pi, 2) to ["$p=2\pi$"]   ++ (2*pi,0);
        
        \begin{scope}[yshift=5.5cm]
            \draw[->] (-1.1*pi,0) -- ++ (5.3*pi,0) node[below left] {$f$};
            \draw[->] (0,-2)      -- ++ (0,5)    node[below left] {$A$};
            % Fonction (courbe périodique)
            \draw[thick]    plot [domain=-pi:4*pi]
            (\x,{0.5*sin(2*\x) + sin(3*\x) + 0.2*sin(4*\x)});   
        \end{scope}
    \end{tikzpicture}
\end{document}

Answer 2

Your code is quit fine, so maybe some minor changes:

• you not need to load tikz twice
• I would use tikz libraries arrows.meta and quotes for a bit nicer arrows heads and simpler draw labels on edge
• using option trig format=rad, make writing equation more simpler
• I wouldn't use smooth option, rather increase number of samples

\documentclass[tikz, border=5pt]{standalone}
\usetikzlibrary{arrows.meta,
                quotes}

\begin{document}
    \begin{tikzpicture}[scale=0.5, 
    >=Stealth,%Latex,
    trig format=rad, % or deg   <------
    samples=201         ]
% Axes
\draw[->] (-1.1*pi,0) -- ++ (4.3*pi,0) node[below left] {$f$};
\draw[->] (0,-2)      -- ++ (0,4.4)    node[below left] {$A$};
% Fonction (courbe périodique)
\draw[thick]    plot [domain=-pi:3*pi]
    (\x,{0.5*sin(2*\x) + sin(3*\x) + 0.2*sin(4*\x)});
% Indication de la période p (approximative)
\draw[|<->|] (0.53, 2) to ["$p$"]   ++ (2*pi,0);
    \end{tikzpicture}
\end{document}

Addendum:
First version of answer just show what OP can do better with result as (s)he show in question. However, idra presented in @Raffaele Santoro answer is interesting. Based on it, I would draw your image on the following way:

\documentclass[tikz, border=5pt]{standalone}
\usetikzlibrary{arrows.meta,
                quotes}

\begin{document}
    \begin{tikzpicture}[scale=0.5, 
    >=Stealth,%Latex,
    trig format=rad, % or deg   <------
    samples=201         ]
% Axes
\draw[->] (-1.1*pi,0) -- ++ (4.3*pi,0) node[below left] {$f$};
\draw[->] (0,-2)      -- ++ (0,4.4)    node[below left] {$A$};
% Fonction (courbe périodique)
\draw[thick,densely dotted]    plot [domain=-pi:3*pi]
    (\x,{0.5*sin(2*\x) + sin(3*\x) + 0.2*sin(4*\x)});
\draw[thick]    plot [domain=0:2*pi]
    (\x,{0.5*sin(2*\x) + sin(3*\x) + 0.2*sin(4*\x)});
% Indication de la période p (approximative)
\draw[<->|, very thin] (0, 1.9) to ["$p$"]   ++ (2*pi,0);
    \end{tikzpicture}
\end{document}