2025 Ahmad Ibrahim Secondary School Prelims A Math Paper 1
It is given that \(f(x)=4+\cos\left(\frac{x}{2}\right)\) and \(g(x)=-2\sin x\).
State the period and amplitude of \(f(x)\).[2]
State the period and amplitude of \(g(x)\).[1]
Sketch, on the same axes, the graphs of \(y=f(x)\) and \(y=g(x)\) for \(0^\circ \le x \le 360^\circ\).[3]
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Answer:(a) Period \(=720^\circ\), amplitude \(=1\). (b) Period \(=360^\circ\), amplitude \(=2\). (c) Sketch \(y=4+\cos(x/2)\) smoothly from \((0^\circ,5)\) to \((360^\circ,3)\) through \((180^\circ,4)\), and sketch \(y=-2\sin x\) through \((0^\circ,0)\), \((90^\circ,-2)\), \((180^\circ,0)\), \((270^\circ,2)\), and \((360^\circ,0)\).