How to draw a sinewave in Tikz?

Question

I am an absolute newbie in LaTeX in general and Tikz in particular and am in the process of exploring various aspects of the ecosystem. During the course of looking Tikz related information I came across this response: Sinewave in Tikz.

This works but I am unable to figure out how this works. Can someone point me or explain how these commands combine to generate a sine wave?

Answer 1

The Last Error has given the snippet from manual and there shouldn't be any error anymore. But still some illustration would be nice. This answer serves that purpose.

Let use consider the construct:

\draw[ultra thick, red] (3,0) sin (4,1)

in

\documentclass[tikz,border=10pt]{standalone}
\begin{document}
    \begin{tikzpicture}
    \draw (0,0) -- (12,0);
    \draw (0.2,1)node[left,font=\tiny] {$y=1$} -- (11.8,1);
    \draw (0.2,-1)node[left,font=\tiny] {$y=-1$} -- (11.8,-1); 
    \foreach \x in {0,0.5,...,12}{
    \draw (\x,-0.2)node [below,font=\tiny,] {\x} -- (\x,0.2) ;
    }
    \draw[ultra thick, red] (3,0) sin (4,1);    %% the real business in this line
    \end{tikzpicture}
\end{document}

It says that starting from the point (3,0) draw a sine curve and end the curve at the point (4,1):

Please note that the sin and cos commands draw only a quarter sine/cos curve and the y coordinate of two points should be different. For example, if you draw

(3,0) sin (11,0)     %%% same y-coordinate

you will get a straight line like:

Now add the line

\draw[ultra thick, blue] (4,1) cos (5,0);    %% the real business in this line

This says that start a cosine curve at (4,1) and end it at (5,0):

The blue curve is the cosine curve. You add sin and cos curves like this continuously and alternatively to get a continuous sine wave:

\documentclass[tikz,border=10pt]{standalone}
\begin{document}
    \begin{tikzpicture}
    \draw (0,0) -- (12,0);
    \draw (0.2,1)node[left,font=\tiny] {$y=1$} -- (11.8,1);
    \draw (0.2,-1)node[left,font=\tiny] {$y=-1$} -- (11.8,-1); 
    \foreach \x in {0,0.5,...,12}{
    \draw (\x,-0.2)node [below,font=\tiny,] {\x} -- (\x,0.2) ;
    }
    \draw[ultra thick, red] (3,0) sin (4,1);    %% the real business in this line
    \draw[ultra thick, blue] (4,1) cos (5,0);    %% the real business in this line
    \draw[ultra thick, red] (5,0) sin (6,-1);    %% the real business in this line
    \draw[ultra thick, blue] (6,-1) cos (7,0);    %% the real business in this line
    \draw[ultra thick, red] (7,0)  sin (8,1);    %% the real business in this line
    \draw[ultra thick, blue] (8,1) cos (9,0);    %% the real business in this line
    \draw[ultra thick, red] (9,0) sin (10,-1);    %% the real business in this line
    \draw[ultra thick, blue] (10,-1) cos (11,0);    %% the real business in this line
    \end{tikzpicture}

\end{document}

All red curves are sine curves and the blue ones are cosines. Instead of putting many separate \draw commands like this, you can stuff all of them in one \draw command:

\draw[ultra thick, red]
    (3,0) sin (4,1) cos (5,0) sin (6,-1) cos (7,0)
          sin (8,1) cos (9,0) sin (10,-1) cos (11,0);

as Peter Grill did in his linked answer

Answer 2

According to Karl's students (who don't care about almost everything in TikZ) on page 30 of TikZ documentation (by invoking texdoc tikz in your terminal, shell, DOS prompt), they said that

Sine

Remember 3 important behaviors:

• sin (x,y) draws only the first 1/4 of a complete sine curve. In other words, the curve in the first quadrant is drawn.

• the previous point is used as the starting point.

• if the previous point is lower than (x,y) then it draws sine with positive amplitude. Otherwise it draws with negative amplitude.

If you still get confused with these 3 rules, the progressive examples as follows should help you understand its behavior.

\begin{tikzpicture}
    \draw[gray] (0,0) grid (5,5);
    \draw[red] (0,0) sin (1,2);
\end{tikzpicture}

\begin{tikzpicture}
    \draw[gray] (0,0) grid (5,5);
    \draw[red] (0,0) sin (1,2) sin (3,5);
\end{tikzpicture}

\begin{tikzpicture}
    \draw[gray] (0,0) grid (5,5);
    \draw[red] (0,0) sin (1,2) sin (3,5) sin (5,0);
\end{tikzpicture}

Cosine

Cosine is the "complement" of sine. The following examples should make it clearer.

\begin{tikzpicture}
    \draw[gray] (0,0) grid (5,5);
    \draw[red] (0,0) sin (1,2);
    \draw[blue] (0,0) cos (1,2);
\end{tikzpicture}

\begin{tikzpicture}
    \draw[gray] (0,0) grid (5,5);
    \draw[red] (0,0) sin (1,2) sin (3,5);
    \draw[blue] (0,0) cos (1,2) cos (3,5);
\end{tikzpicture}

\begin{tikzpicture}
    \draw[gray] (0,0) grid (5,5);
    \draw[red] (0,0) sin (1,2) sin (3,5) sin (5,0);
    \draw[blue] (0,0) cos (1,2) cos (3,5) cos (5,0);
\end{tikzpicture}

Summary

If you want to create a complete sine wave then you need to use both sin and cos alternately as follows,

\begin{tikzpicture}
    \draw[gray] (0,-3) grid (5,3);
    \draw[green] (0,0) sin (1,2) cos (2,0) sin (3,-2) cos (4,0);
\end{tikzpicture}

because using sin alone does not produce what you want to get as follows.

\begin{tikzpicture}
    \draw[gray] (0,-3) grid (5,3);
    \draw[red] (0,0) sin (1,2) sin (2,0) sin (3,-2) sin (4,0);
\end{tikzpicture}