\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{tikz}
\usepackage{geometry}
\geometry{verbose,tmargin=1cm,bmargin=1cm,lmargin=3cm,rmargin=3cm}
\begin{document}
\begin{center}
\begin{tikzpicture}[x=5cm,y=5cm]
\draw[<->] (-1.5,0)--(1.5,0)node[above]{$x$};
\draw[<->] (0,-1.5)--(0,1.5)node[right]{$y$};
\foreach \x in {-1,1}
\draw[shift={(\x,0)}](0pt,2pt)--(0,-2pt)node[below]{\footnotesize $\x$};
\foreach \y in {-1,1}
\draw[shift={(0,\y)}](2pt,0pt)--(-2pt,0pt)node[left]{\footnotesize $\y$};
\draw [color=gray!30,dash pattern=on 1pt off 1pt, xstep=0.1,ystep=0.1] (-1.5,-1.5) grid (1.5,1.5);
\draw[thick,gray!50,xstep=0.5,ystep=0.5](-1.5,-1.5) grid (1.5,1.5);
\foreach \x in {-1.4,-1.3,-1.2,-1.1,-0.9,-0.8,-0.7,-0.6,-0.5,-0.4,-0.3,-0.2,-0.1,0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1,1.1,1.2,1.3,1.4}
\draw(\x,2pt)--(\x,-2pt)node[below,gray!20]{$\x$};
%\draw[shift={(\x,0)}](0pt,2pt)--(0,-2pt)node[color=gray,rotate=90]{\footnotesize $\x$};
%\foreach \y in {-1.4,-1.3,-1.2,-1.1,-0.9,-0.8,-0.7,-0.6,-0.5,-0.4,-0.3,-0.2,-0.1,0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1,1.1,1.2,1.3,1.4}
% \draw(\y,0)node[below,gray!30]{$\y$};
%\draw[shift={(0,\y)}](2pt,0pt)--(-2pt,0pt)node[color=gray,left]{\footnotesize $\y$};
\draw (0,0) circle (1);
\foreach \x in {0,10,...,360}
\draw[dashed,color=blue] (0,0)--(\x:1);
\foreach \x in {0,10,...,360}
\draw [dashed,fill=blue] (\x:1) circle (1.5pt)node[sloped,above]{$\x$};
\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:5.75cm) node[above] {$\xtext$};
\foreach \x in {0,30,...,360}
\draw[dashed,color=red] (0,0)--(\x:5.5cm);
\foreach \x in {0,45,...,360}
\draw[dashed,color=red] (0,0)--(\x:5.5cm);
\end{tikzpicture}
\end{center}
\end{document}
