Code:
\documentclass[tikz]{standalone}
\usetikzlibrary{intersections}
\newcounter{angle}
\setcounter{angle}{60}
\newlength\xperdeg
\setlength\xperdeg{0.166667mm}% Breite der Sinuskurve / Vollkreis (6cm/360°)
\begin{document}
\begin{tikzpicture}
\draw[black!20] (0,1.5) -- +(4.5,0) %Projektierungslinien
(0,-1.5) -- +(7.5,0)
(2,0) -- (3,0)
(-1.5,0) -- +(0,-6)
(1.5,0) -- +(0,-9)
(0,-2) -- (0,-3);
\draw[thick,->] (-2,0)--(2,0) node[below] {$x$};
\draw[thick,->] (0,-2)--(0,2) node[left] {$y$};
\draw[red,thick] (0,0) circle (1.5cm);
\draw (1.6,0) node[red, below]{1};
\draw (0,1.65) node[red,left]{1};
%
\draw[ultra thick,cyan] (0,0) -- (0,0 |- \theangle:1.5cm); % Siehe `texdoc pgfmanual', Abschnitt ``Intersections of Perpendicular Lines''
\draw[ultra thick,orange] (0,0) -- (\theangle:1.5cm |- 0,0);
%
\draw[densely dotted,orange] (\theangle:1.5cm) -- (\theangle:1.5cm |- 0,0);
\draw[densely dotted,cyan] (\theangle:1.5cm) -- (0,0 |- \theangle:1.5cm);
\draw[ultra thick,red,->,rotate=\theangle] (0,0) -- (1.5,0);
\draw[->] (0.5,0) arc [start angle=0, delta angle=\theangle, radius=0.5cm];
% \draw (0.75,0.25) node[anchor= south west]{$\;\varphi = \omega t + \varphi_0$};
\draw[orange] (2,2) node {\theangle$^\circ$};
\fill[black] (0,0) circle (1mm);
\draw[->] (3,-2) -- +(0,4) node[left]{$y$};% für die Sinuskurve
\draw[->] (3,0) -- +(6.5,0) node[below]{$t$};
\draw[->] (-2,-3) -- +(4,0) node[above]{$y$};% für die Kosinuskurve
\draw[->] (0,-3) -- +(0, -6.5) node[left]{$t$};
\draw[blue,xshift=2.9999cm, x=1.50005cm, y=1.5cm, name path=sine curve] (0,0) sin (1,1) cos (2,0) sin (3,-1) cos (4,0);
\draw[red, yshift=-2.9999cm, rotate=-90, x=1.50005cm, y=1.5cm, name path=cosine curve] (0,1) cos (1,0) sin (2,-1) cos (3,0) sin (4,1);
\path[name path=proj sline] (\theangle\xperdeg, -2) ++(3,0) -- +(0,4);
\path[name path=proj cline] (-2, -\theangle\xperdeg) ++(0,-3) -- +(4,0);
\draw[name intersections={of=sine curve and proj sline}, cyan]
(3,0) +(\theangle\xperdeg,0) -- (intersection-1) -- (\theangle:1.5cm);
\draw (intersection-1) circle[radius=0.5mm];
\draw[name intersections={of=cosine curve and proj cline}, orange]
(0,-3) +(0,-\theangle\xperdeg) -- (intersection-1) -- (\theangle:1.5cm);
\draw (intersection-1) circle[radius=0.5mm];
\end{tikzpicture}
\end{document}
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