State the range of principal values of $\tan^{-1} x$.[1] The curve $y=a+b\cos cx$ is shown below

Question

State the range of principal values of $\tan^{-1} x$.[1] The curve $y=a+b\cos cx$ is shown below for $0\leq x\leq \dfrac{3\pi}{2}$ radians. The curve has maximum points at $\left(\dfrac{\pi}{2},7\right)$ and $\left(\dfrac{3\pi}{2},7\right)$. The curve also has minimum points at $(0,1)$ and $(\pi,1)$. Find the values of $a$, $b$ and $c$.[3] On the same axes, draw a straight line to determine the number of solutions for the equation $a\pi+b\pi\cos cx=5\pi-2x$ for $0\leq x\leq \dfrac{3\pi}{2}$.[3]

Accepted Answer

(a) $-\dfrac{\pi}{2}<\tan^{-1}x<\dfrac{\pi}{2}$ (b)(i) $a=4,\ b=-3,\ c=2$ (ii) $3$ solutions

2025 CGSS PRELIMS P1 Q4

2025 CGSS PRELIMS P1 Q4

Solution:

Solution locked