\begin{tikzpicture}[
  my angle/.style={
    draw, <->,
    angle eccentricity=1.3,
    angle radius=9mm
  }
]

% coordinate axis
\draw[<->] (-2.5,0) -- (2.5,0);
\draw[<->] (0,-2.5) -- (0,2.5);

% circle
\draw (0,0) circle (2cm);

% coordinates
\coordinate (A)  at ( 2,0);
\coordinate (B)  at ( 0,2);
\coordinate (C)  at (-2,0);
\coordinate (D)  at (0,-2);

%
\coordinate                 (O) at ( 0:0);

\draw (C) node[anchor=north east] {-1};

% angles
\shorthandoff{"}
\pic[my angle, "$-\pi$"]      {angle = C--O--A};
\pic[my angle, "$\pi$"]      {angle = A--O--C};
\shorthandon{"}

% \coordinate[pin=300:{$(0,-1)$}] (sinTheta) at (C);
\end{tikzpicture}