Sketch, on the same diagram, the curves $y = 3\cos x$ and \(y = 1 - 2\sin\left(\frac{2x}{3}\right)

Question

Sketch, on the same diagram, the curves $y = 3\cos x$ and $y = 1 - 2\sin\left(\frac{2x}{3}\right)$ for $0 \le x \le 3\pi$.[3] Hence, find the number of distinct values of $x$ for $0 \le x \le 3\pi$, for which $3\cos x + 2\sin\left(\frac{2x}{3}\right) = 1$.[1] $3\cos{3x} + 2\sin{2x} = 1$.[1]

Accepted Answer

(a) Both restricted curves shown. (b)(i) $3$. (b)(ii) $9$.

2024 GESS PRELIMS P1 Q10

2024 GESS PRELIMS P1 Q10

Solution:

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