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 sin
e 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 cos
ine 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
frequency
andamplitude
you wish to know is another Q due tophase
difference of learning :) I am suretexdoc tikz
would be too exhaustive may be start with csweb.ucc.ie/~dongen/LAF/TikZ.pdf and Related Links at tex.stackexchange.com/questions/15779/…