\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);

  % angles
  \shorthandoff{"}
  \pic[my angle, "$\frac{-\pi}{2}$"]      {angle = D--O--A};
  \shorthandon{"}

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