On the coordinate plane, $O$ is the origin, and points $A(1,0)$ and $B(-2,0)$ are given. There are also two points $P$ and $Q$ in the upper half-plane satisfying $\overline{AP} = \overline{OA}$, $\overline{BQ} = \overline{OB}$, $\angle POQ$ is a right angle. Let $\angle AOP = \theta$. The length of line segment $\overline{OP}$ is which of the following options? (Single choice question, 3 points) (1) $\sin\theta$ (2) $\cos\theta$ (3) $2\sin\theta$ (4) $2\cos\theta$ (5) $\cos 2\theta$
On the coordinate plane, $O$ is the origin, and points $A(1,0)$ and $B(-2,0)$ are given. There are also two points $P$ and $Q$ in the upper half-plane satisfying $\overline{AP} = \overline{OA}$, $\overline{BQ} = \overline{OB}$, $\angle POQ$ is a right angle. Let $\angle AOP = \theta$.
The length of line segment $\overline{OP}$ is which of the following options? (Single choice question, 3 points)\\
(1) $\sin\theta$\\
(2) $\cos\theta$\\
(3) $2\sin\theta$\\
(4) $2\cos\theta$\\
(5) $\cos 2\theta$