Diagramming Unit Circle and Sine Wave with TikZ

Question

How could I express this diagram (attached) as a TikZ picture to be used in a LaTeX document? I've been working on it for a while with no success.

Thank you for your help.

\documentclass{article}% guessing (cfr)
\usepackage{tikz}
\usepackage[top=1in,bottom=1in,right=1in,left=1in]{geometry}
\begin{document}% added - surely necessary! (cfr)
\begin{tikzpicture}[scale=5.3,cap=round,>=latex]
        \draw[->] (-1.5cm,0cm) -- (1.5cm,0cm) node[right,fill=white] {$x$};
        \draw[->] (0cm,-1.5cm) -- (0cm,1.5cm) node[above,fill=white] {$y$};

        \draw[thick] (0cm,0cm) circle(1cm);

        \foreach \x in {0,30,...,360} {
                \draw[gray] (0cm,0cm) -- (\x:1cm);
                \filldraw[black] (\x:1cm) circle(0.4pt);
                \draw (\x:0.6cm) node[fill=white] {$\x^\circ$};
        }

        \foreach \x/\xtext in {
            30/\frac{\pi}{6},
            45/\frac{\pi}{4},
            60/\frac{\pi}{3},
            90/\frac{\pi}{2},
            120/\frac{2\pi}{3},
            135/\frac{3\pi}{4},
            150/\frac{5\pi}{6},
            180/\pi,
            210/\frac{7\pi}{6},
            225/\frac{5\pi}{4},
            240/\frac{4\pi}{3},
            270/\frac{3\pi}{2},
            300/\frac{5\pi}{3},
            315/\frac{7\pi}{4},
            330/\frac{11\pi}{6},
            360/2\pi}
                \draw (\x:0.85cm) node[fill=white] {$\xtext$};

        \foreach \x/\xtext/\y in {
            30/\frac{\sqrt{3}}{2}/\frac{1}{2},
            45/\frac{\sqrt{2}}{2}/\frac{\sqrt{2}}{2},
            60/\frac{1}{2}/\frac{\sqrt{3}}{2},
            150/-\frac{\sqrt{3}}{2}/\frac{1}{2},
            135/-\frac{\sqrt{2}}{2}/\frac{\sqrt{2}}{2},
            120/-\frac{1}{2}/\frac{\sqrt{3}}{2},
            210/-\frac{\sqrt{3}}{2}/-\frac{1}{2},
            225/-\frac{\sqrt{2}}{2}/-\frac{\sqrt{2}}{2},
            240/-\frac{1}{2}/-\frac{\sqrt{3}}{2},
            330/\frac{\sqrt{3}}{2}/-\frac{1}{2},
            315/\frac{\sqrt{2}}{2}/-\frac{\sqrt{2}}{2},
            300/\frac{1}{2}/-\frac{\sqrt{3}}{2}}
                \draw (\x:1.25cm) node[fill=white] {$\left(\xtext,\y\right)$};

        \draw (-1.25cm,0cm) node[above=1pt] {$(-1,0)$}
              (1.25cm,0cm)  node[above=1pt] {$(1,0)$}
              (0cm,-1.25cm) node[fill=white] {$(0,-1)$}
              (0cm,1.25cm)  node[fill=white] {$(0,1)$};
    \end{tikzpicture}
\end{document}

Which came out as

Answer 1

A beginning, maybe.

EDIT This version combines the two pictures I used in the original version, and uses backgrounds to demonstrate how to add the dashed lines. Two such lines are drawn to illustrate the method. (It isn't terribly tidy but the lines do appear in the intended places.)

EDIT 2 This version draws more lines via a loop and adds the perpendiculars down to the x axis.

\documentclass[a4paper]{article}% guessing (cfr)
\usepackage[landscape,scale=.9]{geometry}
\usepackage{tikz}
\usetikzlibrary{datavisualization.formats.functions,backgrounds,calc}
\def\mytypesetter#1{% page 813
  \pgfmathparse{#1/pi}%
  \pgfmathprintnumber{\pgfmathresult}$\pi$%
}
\begin{document}% added - surely necessary! (cfr)
  \centering
  \begin{tikzpicture}[scale=4,cap=round,>=latex,baseline={(0,0)}]
    \draw[->] (-1.5cm,0cm) -- (1.5cm,0cm) node[right,fill=white] {$x$};
    \draw[->] (0cm,-1.5cm) -- (0cm,1.5cm) node[above,fill=white] {$y$};

    \draw[thick] (0cm,0cm) circle(1cm);

    \foreach \x in {0,30,...,360} {
      \draw[gray] (0cm,0cm) -- (\x:1cm);
      \filldraw[black] (\x:1cm) coordinate (x\x) circle (0.4pt);
      \draw (\x:0.6cm) node[fill=white] {$\x^\circ$};
    }

    \foreach \x/\xtext in {
      30/\frac{\pi}{6},
      45/\frac{\pi}{4},
      60/\frac{\pi}{3},
      90/\frac{\pi}{2},
      120/\frac{2\pi}{3},
      135/\frac{3\pi}{4},
      150/\frac{5\pi}{6},
      180/\pi,
      210/\frac{7\pi}{6},
      225/\frac{5\pi}{4},
      240/\frac{4\pi}{3},
      270/\frac{3\pi}{2},
      300/\frac{5\pi}{3},
      315/\frac{7\pi}{4},
      330/\frac{11\pi}{6},
      360/2\pi}
    \draw (\x:0.85cm) node[fill=white] {$\xtext$};

    \foreach \x/\xtext/\y in {
      30/\frac{\sqrt{3}}{2}/\frac{1}{2},
      45/\frac{\sqrt{2}}{2}/\frac{\sqrt{2}}{2},
      60/\frac{1}{2}/\frac{\sqrt{3}}{2},
      150/-\frac{\sqrt{3}}{2}/\frac{1}{2},
      135/-\frac{\sqrt{2}}{2}/\frac{\sqrt{2}}{2},
      120/-\frac{1}{2}/\frac{\sqrt{3}}{2},
      210/-\frac{\sqrt{3}}{2}/-\frac{1}{2},
      225/-\frac{\sqrt{2}}{2}/-\frac{\sqrt{2}}{2},
      240/-\frac{1}{2}/-\frac{\sqrt{3}}{2},
      330/\frac{\sqrt{3}}{2}/-\frac{1}{2},
      315/\frac{\sqrt{2}}{2}/-\frac{\sqrt{2}}{2},
      300/\frac{1}{2}/-\frac{\sqrt{3}}{2}}
    \draw (\x:1.25cm) node {$\left(\xtext,\y\right)$};

    \draw (-1.25cm,0cm) node[above=1pt] {$(-1,0)$}
    (1.25cm,0cm)  node[above=1pt] {$(1,0)$}
    (0cm,-1.25cm) node[fill=white] {$(0,-1)$}
    (0cm,1.25cm)  node[fill=white] {$(0,1)$};
    \begin{scope}[xshift=20mm]
      \datavisualization
      [
      school book axes,
      y axis={unit length=10mm},
      x axis={unit length=2.5mm, ticks={step=(.5*pi), tick typesetter/.code=\mytypesetter{##1}}},
      visualize as smooth line,
      ]
      data [format=function] {
        var x : interval [0:4*pi];
        func y = sin(\value x r);
      };
    \end{scope}
    \begin{scope}[on background layer]
      \coordinate (o) at (0,0);
      \foreach \i in {90,120,...,270}
        {
          \draw [densely dashed, opacity=.25, color=blue!50!cyan] (x\i) -- ({x\i} -| o) -- ++(20mm,0) -- ++(pi*\i/720,0) coordinate (xx\i) edge (xx\i |- o)  -- ++(.5*pi,0) coordinate (xxx\i) edge (xxx\i |- o);
        }
    \end{scope}
  \end{tikzpicture}
\end{document}