2026 NASS P2 Q5

2026 NASS P2 Q5

Secondary 4
5 marks

Given that \(b>0\), the graph of \(y=a\cos(bx)+c\) has adjacent minimum points at \((0,-1)\) and \((4\pi,-1)\). It also has a maximum point at \((2\pi,5)\).

  1. Find the values of \(a\), \(b\) and \(c\).[3]
  2. Hence sketch the graph of \(y=a\cos(bx)+c\) for \(0\le x\le\pi\).[2]

Solution:

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Answer:(a) \(a=-3,b=\dfrac12,c=2\). (b) Increasing cosine arc from \((0,-1)\) to \((\pi,2)\).

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