2025 DSS PRELIMS P1 Q11
2025 DSS PRELIMS P1 Q11
Secondary 4
6 marks
- Sketch the graphs of \( y=-2\cos 3x+1 \) and \( y=-\frac{2}{\pi}x+1 \) on the same axes, for \( 0\le x\le \pi \).[5]
- Explain how the number of solutions for \( 2\cos 3x=\frac{2}{\pi}x \) can be found using the graphs.[1]
Solution:
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Answer:(a) Sketch \(y=-2\cos3x+1\) through \((0,-1),\left(\frac{\pi}{6},1\right),\left(\frac{\pi}{3},3\right),\left(\frac{\pi}{2},1\right),\left(\frac{2\pi}{3},-1\right),\left(\frac{5\pi}{6},1\right),(\pi,3)\), together with the line segment \(y=-\frac{2}{\pi}x+1\) from \((0,1)\) to \((\pi,-1)\). (b) \(3\) solutions.
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