4

Consider the functions $f(x)=\cos x$ and $g(x)=\sin 2x$, where $0\le x\le\pi$.
The graph of $f$ intersects the graph of $g$ at the point $A$, the point $B\;(\pi/2,0)$ and the point $C$ as shown below.

(a) Find the $x$-coordinate of point $A$ and the $x$-coordinate of point $C$.

The shaded region $R$ is enclosed by the graph of $f$ and the graph of $g$ between the points $B$ and $C$.

(b) Find the area of $R$.