[Tex/LaTex] Use tikz to plot sine wave with text and lines

Question

I wanted to get a tikz plot to look like:

I am getting two cycles in my code. The original code was masterfully written by moospit found here. Here is the code to start with:

\documentclass[tikz, border=5mm]{standalone}

\usetikzlibrary{datavisualization.formats.functions, arrows}

\def\mytypesetter#1{
  \pgfmathparse{#1/pi}
  \pgfkeys{/pgf/number format/precision=2}
  \pgfmathroundtozerofill{\pgfmathresult}
  \pgfmathifisint{\pgfmathresult}{
    \pgfmathprintnumber{\pgfmathresult}$\pi$
  }{
    \pgfmathprintnumber[/pgf/number format/frac, frac whole=false]{\pgfmathresult}$\pi$
  }
}

\begin{document}
  \begin{tikzpicture}
    \datavisualization [
      school book axes,
      all axes={
        grid={
          major={style={red!50!black, opacity=.25}},
          minor={style={green!25!black, opacity=.25}},
          minor steps between steps=3,
      }},
      x axis={
        label=$\phi$,
        ticks and grid={
          stack,
          step=(2*pi),
          tick typesetter/.code=\mytypesetter{##1},
      }},
      y axis={
        label=$v$,
        grid={step=1}
      },
      style sheet=vary hue,
      visualize as line/.list={sin1}
    ]
    data [set=sin1, format=function] {
      var x : interval [-2*pi:2*pi] samples 100;
      func y = sin(\value x r);
    };
  \end{tikzpicture}
\end{document} 

Answer 1

I am not very familiar with the datavisualization of tikz. So I recreated your picture with pgfplots.

\documentclass[border=5mm]{standalone}

\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
    \begin{axis}[
        height=6cm,
        width=13cm,
        axis lines=middle,
        grid=both,
        domain={-360:360},
        ymin=-1.3, ymax=1.3,
        xmin=-400, xmax=400,
        major tick length=1ex,
        minor tick length=0pt,
        tick style={color=black,thin},
        xtick={-360, 360},
        xticklabels={$-2\pi$, $2\pi$},
        minor xtick={-360,-270,...,360},
        xlabel=$\phi$,
        every axis x label/.style={
            at={(ticklabel* cs:1)},
            anchor=west,
        },
        xticklabel shift={.2cm},
        ytick={-1,1},
        yticklabels={$-1$, $1$},
        minor ytick={-0.5,0.5},
        ylabel=$v$,
        every axis y label/.style={
            at={(ticklabel* cs:1)},
            anchor=south,
        },
        ]
    \addplot[thin, dashed] coordinates { (80, 0) (80, 0.642788) (0, 0.642788) };
    \addplot[thick, black, samples=100] { sin(0.5*x) };
    \addplot+[mark=*, color=black, mark options={scale=0.75,fill=black}] coordinates { (80, 0.642788) };
    \node at (axis cs:0,0.642788) [anchor=east] {$\sigma_v$};
    \node at (axis cs:80,0) [anchor=north] {$\sigma_\phi$};
    \end{axis}
\end{tikzpicture}
\end{document}

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Output: