Question 8
The equation of a curve is $y = 4\cos 2x + 3$ for $0 \le x \le 2\pi$.
**(c)** Hence determine the number of solutions of the equation $4\cos 2x + 3 = 2x - 1$ for $0 \le x \le 2\pi$.
(In part (b) you sketched $y = 4\cos 2x + 3$: two cycles with maxima 7 at $x = 0, \pi, 2\pi$ and minima −1 at $x = \frac{\pi}{2}, \frac{3\pi}{2}$.)
**(c)** Hence determine the number of solutions of the equation $4\cos 2x + 3 = 2x - 1$ for $0 \le x \le 2\pi$.
(In part (b) you sketched $y = 4\cos 2x + 3$: two cycles with maxima 7 at $x = 0, \pi, 2\pi$ and minima −1 at $x = \frac{\pi}{2}, \frac{3\pi}{2}$.)
