Problem

The equation of a curve is $y = 4\cos 2x + 3$ for $0 \leq x \leq 2\pi$.

(a) State the greatest and least possible values of $y$.

(b) Sketch the curve.

(c) Hence determine the number of solutions of the equation $4\cos 2x + 3 = 2x - 1$ for $0 \leq x \leq 2\pi$.