1.41: Past-paper question 1

Figure 1 shows sector $\displaystyle ROS$ of a circle with centre $\displaystyle O$ and radius 2 cm
The size of angle $\displaystyle ROS$ is $\displaystyle \theta$ radians.

The area of sector $\displaystyle ROS$ is $\displaystyle \frac{\pi}{2} \mathrm{cm}^2$

(a) Find the exact value of $\displaystyle \theta$

The perimeter of sector $\displaystyle ROS$ is $\displaystyle P \mathrm{cm}$

(b) Find the exact value of $\displaystyle P$