Problem

Figure 2 shows a plot of part of the curve with equation $y=\cos2x$ with $x$ being measured in radians.

Figure 2

The point $P$, shown on Figure 2, is a minimum point on the curve.

(a) State the coordinates of $P$.

A copy of Figure 2, called Diagram 1, is shown at the top of the next page.

Diagram 1

(b) Sketch, on Diagram 1, the curve with equation $y=\sin x$.

(c) Hence, or otherwise, deduce the number of solutions of the equation

(i) $\cos2x=\sin x$ that lie in the region $0\leq x\leq20\pi$,

(ii) $\cos2x=\sin x$ that lie in the region $0\leq x\leq21\pi$.