The function $\mathrm{f}$ is defined, for $0^{\circ} \le x \le 180^{\circ}$, by \(\mathrm{f

Question

The function $\mathrm{f}$ is defined, for $0^{\circ} \le x \le 180^{\circ}$, by $\mathrm{f}(x) = c + a \cos bx$, where $a$, $b$ and $c$ are positive integers. Given that the amplitude of $\mathrm{f}$ is 4 and the period of $\mathrm{f}$ is $120^{\circ}$, state the value of $a$ and of $b$,[2] Given that the minimum value of $\mathrm{f}$ is $-5$, find the value of $c$,[1] sketch the graph of $y = \mathrm{f}(x)$ for $0^{\circ} \le x \le 180^{\circ}$.[3] A line $y = k$ is drawn on the graph of $y = \mathrm{f}(x)$. State the range of values of $k$ that will give 3 intersections.[1]

Accepted Answer

(i) $a = 4, b = 3$ (ii) $c = -1$ (iv) $ -5 < k < 3$

2024 CCHY P1 Q9

2024 CCHY P1 Q9