LaTeX Forum

\documentclass{article}

\usepackage{pgfplots}
\pgfplotsset{compat=1.15}

\begin{document}
\begin{tikzpicture}[scale=1,>=latex]
\begin{axis}[
    trig format plots=rad,
    axis equal,
    ymin=0, ymax = 250,
    xmin=0, xmax=200,
    hide axis
]
\draw[blue, fill=blue] (60.46181719,163.8889268) circle [blue, radius=1];
\addplot [domain=0 : 0.125*pi*0.9, samples=200, black] ({sin(x)*(179-0.8*(1/(cos(4*x))-1))}, {cos(x)*(179-0.8*(1/(cos(4*x))-1))});
%Tangente
\addplot[black, domain=50:80] {163.889 - 1.52393*(-60.4618 + x)};
%Orthogonale
\addplot[black, domain=0:90] {163.889 - 0.656199*(60.4618 - x)};
%Gerade 22.5°
\addplot[black, domain=0:80] {tan(pi/2-0.125*pi)*x};
\addplot [domain=0:2*pi, samples=50, red] ({70.6558+12.1928*cos(x)}, {170.578+12.1928*sin(x)});
\addplot [domain=1.18*pi:1.38*pi, samples=50, green] ({70.6558+12.1928*cos(x)}, {170.578+12.1928*sin(x)});
\draw (0,0) -- (0,179);
\draw (0,0) -- (60.46181719,163.8889268);
\draw[->] (30,100) arc (80:30:35);
\end{axis}
\end{tikzpicture}
\end{document}

\documentclass[border=20pt]{standalone} 
\usepackage{pgfplots} 
\pgfplotsset{compat=newest} 
\usepgfplotslibrary{fillbetween}
\begin{document} 
\begin{tikzpicture}[scale=1,>=latex] 
\begin{axis}[ 
    trig format plots=rad, 
    axis equal, 
    ymin=0, ymax = 250, 
    xmin=0, xmax=200, 
    hide axis 
] 
\draw[blue, fill=blue] (60.46181719,163.8889268) circle [blue, radius=1]; 
\addplot [domain=0 : 0.125*pi*0.9, samples=200, black, name path = top]
  ({sin(x)*(179-0.8*(1/(cos(4*x))-1))}, {cos(x)*(179-0.8*(1/(cos(4*x))-1))}); 
%Tangente 
\addplot[black, domain=50:80] {163.889 - 1.52393*(-60.4618 + x)}; 
%Orthogonale 
\addplot[black, domain=0:90] {163.889 - 0.656199*(60.4618 - x)}; 
%Gerade 22.5° 
\addplot[black, domain=0:80] {tan(pi/2-0.125*pi)*x}; 
\addplot [domain=0:2*pi, samples=50, red] ({70.6558+12.1928*cos(x)},
  {170.578+12.1928*sin(x)}); 
\addplot [domain=1.18*pi:1.38*pi, samples=50, green] ({70.6558+12.1928*cos(x)},
  {170.578+12.1928*sin(x)}); 
\path[name path = left, draw] (0,0) -- (0,179); 
\path[name path = right, draw] (0,0) -- (60.46181719,163.8889268); 
\draw[->] (30,100) arc (80:30:35); 
\addplot[gray!30] fill between[of=top and right];
\end{axis} 
\end{tikzpicture} 
\end{document}