2025 WGS P1 Q11

2025 WGS P1 Q11

Secondary 4
6 marks
  1. Write \(2\sin\theta+3\cos\theta\) in the form \(R\sin(\theta+\alpha)\), where \(R>0\) and \(0^\circ\le\alpha\le90^\circ\).[3]
  2. Hence find the greatest value of \(2\sin\theta+3\cos\theta-1\), giving your answer in exact value.[1]
  3. Determine the value of \(\theta\) for \(0^\circ\le\theta\le180^\circ\) at which the greatest value occurs.[2]

Solution:

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Answer:(a) \(\sqrt{13}\sin(\theta+56.3^\circ)\). (b) \(\sqrt{13}-1\). (c) \(33.7^\circ\).

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