2025 PHS P2 Q1

2025 PHS P2 Q1

Secondary 4
5 marks

The graph of \(y=a\cos bx+c\) where \(a>0\), has an amplitude of 4 and period of \(\pi\).

  1. State the value of \(a\) and \(b\).[2]
  2. Given that the maximum value of \(y\) is 7, find the value of \(c\).[1]
  3. Sketch the graph of \(y=a\cos bx+c\) for \(0\le x\le2\pi\).[2]

Solution:

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Answer:(a) \(a=4\), \(b=2\) conventionally (also \(-2\)). (b) \(c=3\). (c) Two cosine cycles, maximum 7 and minimum \(-1\).

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