trigonometric tikz

Question

I modified someone's code and get the trigonometric graph I want. But I wonder if there is an easier/elegant code than this.

Specifically, I'd like to have an automatic node setting instead of listing them all. Also, is there an easier way to graph a trig function? I found the addplot feature but it doesn't seem to work in the current code/environment (which is what I prefer).

Thank you.

      \documentclass[oneside]{book}
      \usepackage{amsmath, amsthm}
      \usepackage{forloop, tikz, realboxes}

        \usepackage{tikz}
        \begin{document}
      \begin{tikzpicture}[x=1cm,y=1.5cm]
      \def\xmin{-2*pi}
      \def\xmax{2*pi}
      \def\ymin{-2}
      \def\ymax{2}

      % grid
      \draw[style=help lines, ystep=1, xstep=pi/4] (\xmin,\ymin) grid (\xmax,\ymax);

      % axes
      \draw[thick, ->] (\xmin-.25,0) -- (\xmax+.25,0) node[right] {$x$};
      \draw[thick, ->] (0,\ymin-.25) -- (0,\ymax+.25) node[above] {$y$};

      % xticks and yticks
      \foreach \x in {-6.28319,-5.4978, ..., 6.28319}{
        \draw (\x,2pt) -- (\x,-2pt);
        \node[fill=white] at (-2*pi, -.2) [below] {{$- 2\pi$}};
        \node[fill=white] at (-7*pi/4, -.1) [below] {\tiny{$\dfrac{-7\pi}{4}$}};
        \node[fill=white] at (-3*pi/2, -.1) [below] {\tiny{$\dfrac{-3\pi}{2}$}};
        \node[fill=white] at (-5*pi/4, -.1) [below] {\tiny{$\dfrac{-5\pi}{4}$}};
        \node[fill=white] at (-pi, -.2) [below] {{$-\pi$}};
        \node[fill=white] at (-3*pi/4, -.1) [below] {\tiny{$\dfrac{-3\pi}{4}$}};
        \node[fill=white] at (-pi/2, -.1) [below] {\tiny{$\dfrac{-\pi}{2}$}};
        \node[fill=white] at (-pi/4, -.1) [below] {\tiny{$\dfrac{-\pi}{4}$}};
        %
        \node[fill=white]  at (2*pi, -.2) [below] {{$2\pi$}};
        \node[fill=white]  at (7*pi/4, -.1) [below] {\tiny{$\dfrac{7\pi}{4}$}};
        \node[fill=white]  at (3*pi/2, -.1) [below] {\tiny{$\dfrac{3\pi}{2}$}};
        \node[fill=white]  at (5*pi/4, -.1) [below] {\tiny{$\dfrac{5\pi}{4}$}};
        \node[fill=white]  at (pi, -.2) [below] {{$\pi$}};
        \node[fill=white]  at (3*pi/4, -.1) [below] {\tiny{$\dfrac{3\pi}{4}$}};
        \node[fill=white]  at (pi/2, -.1) [below] {\tiny{$\dfrac{\pi}{2}$}};
        \node[fill=white]  at (pi/4, -.1) [below] {\tiny{$\dfrac{\pi}{4}$}};                                
        }

      \foreach \y in { -2, -1, 1, 2}
        \draw (2pt, \y) -- (-2pt, \y);
      \foreach \y in {-2, -1, 1, 2}
        \node[fill=white] at (-.1,\y) [left] {\y};

    \draw[ultra thick, red]
        (-2*pi-pi/4,1) sin (-3*pi/2-pi/4,2) cos (-pi-pi/4,1) sin (-pi/2-pi/4,0) cos (0-pi/4,1)
        sin (pi/2-pi/4,2) cos (pi-pi/4,1) sin (3*pi/2-pi/4,0) cos (2*pi-pi/4,1) sin (5*pi/2-pi/4,2);

    \end{tikzpicture}
    \end{document}

That is, instead of

\draw[ultra thick, red]
        (-2*pi,0) sin (-3*pi/2,1) cos (-pi,0) sin (-pi/2,-1) cos (0,0)
        sin (pi/2,1) cos (pi,0) sin (3*pi/2,-1) cos (2*pi,0);

I'd like to use something like this:

\draw[scale=1,domain=-1.5:3.5,smooth,variable=\x,blue, thick] plot ({\x},{sin \x});

Answer 1

This is very basic. Obviously you need to adjust the tick labels etc. for your purposes. But you want code which looks something like this:

\documentclass[tikz, border=5pt]{standalone}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\begin{axis}% ref: http://tex.stackexchange.com/a/147772/ by Harish Kumar
\addplot
  [
    domain=-0:2*pi,
    smooth,
    blue,
    thick,
  ]
  plot {sin(deg(x))};
\end{axis}
\end{tikzpicture}
\end{document}

EDIT

Here is a beginning which illustrates how to think about creating the kind of thing you want. That is, I try to demonstrate the approach you want to use here to make this work.

Basically, if you want to draw everything yourself so that you have complete and direct control over labelling, lines, grids etc., then you can do that. But you need in that case to plot the function yourself, too. Or you have to figure out a way to get the plotted function to align with the axes etc. Since that is exactly what \addplot etc. are designed to do, this seems to be reinventing the wheel, but it is, at the end of the day, your wheel.

On the other hand, if you want to be able to use the kind of syntax you indicated in your question to plot the function, then you need \addplot etc. and you need to use its facilities to configure the axes, labels etc. the way you want.

I used several references in working on this - some from the manual for pgfplots and some questions for this site. I've indicated the questions and their authors in the code as comments, and included pages for the most important points I used from the manual.

\documentclass[tikz,border=10pt]{standalone}
\usepackage{pgfplots,mathtools}
\pgfplotsset{compat=1.12}
\begin{document}
\begin{tikzpicture}
  \begin{axis}
    [% 290 of manual
      xtick={-7.0686,-6.2831,...,7.0686},
      xticklabels={% ref:http://tex.stackexchange.com/a/34958/ by Peter Grill
        ,
        {$-2\pi$},
        {\tiny$-\frac{7\pi}{4}$},
        {\tiny$-\frac{3\pi}{2}$},
        {\tiny$-\frac{5\pi}{4}$},
        {$-\pi$},
        {\tiny$-\frac{3\pi}{4}$},
        {\tiny$-\frac{\pi}{2}$},
        {\tiny$-\frac{\pi}{4}$},
        {$0$},
        {\tiny$\frac{\pi}{4}$},
        {\tiny$\frac{\pi}{2}$},
        {\tiny$\frac{3\pi}{4}$},
        {$\pi$},
        {\tiny$\frac{5\pi}{4}$},
        {\tiny$\frac{3\pi}{2}$},
        {\tiny$\frac{7\pi}{4}$},
        {$2\pi$},
      },
      grid=major,
      x=10mm,
      y=20mm,
      axis x line=center,% 218
      axis y line=center,
      xlabel={$x$},
      ylabel={$y$},
      every tick label/.style={fill=white},% 309
    ]
  \addplot% ref: http://tex.stackexchange.com/a/147772/ by Harish Kumar
    [
      domain=-2.25*pi:2.25*pi,
      smooth,
      blue,
      thick,
    ]
    plot {sin(deg(x))};
  \end{axis}
\end{tikzpicture}
\end{document}