
\begin{center}
\begin{tikzpicture}[scale=3.5]
\draw[dotted] (-1,-1) grid[step=0.1] (1,1);
\draw[very thick] (0,0) circle (1cm);
\draw[very thick,->,>=latex] (-1.1,0) -- (1.1,0);
\draw[very thick,->,>=latex] (0,-1.1) -- (0,1.1);
\node[below left] at (0,0) {0};
\node[below right] at (1,0) {1};
\node[above right] at (0,1) {1};
%
\fill[orange] ({-5*180/6}:1) circle (0.5pt) node[below left] {$-\frac{5\pi}{6}$};
\fill[red] ({7*180/4}:1) circle (0.5pt) node[below right] {$\frac{7\pi}{4}$};
\fill[blue] (60:1) circle (0.5pt) node[above right] {$\frac{\pi}{3}$};
\fill[green!50!black] (45:1) circle (0.5pt) node[above right] {$\frac{\pi}{4}$};
\fill[orange] (30:1) circle (0.5pt) node[above right] {$\frac{\pi}{6}$};
\fill[purple] ({2*180/3}:1) circle (0.5pt) node[above left] {$\frac{2\pi}{3}$};
\fill[violet] ({-3*180/4}:1) circle (0.5pt) node[below left] {$-\frac{3\pi}{4}$};
\fill[brown] ({-13*180/3}:1) circle (0.5pt) node[below right] {$-\frac{13\pi}{3}$};
\end{tikzpicture}
\end{center}
