2025 SST PRELIMS P2 Q6

2025 SST PRELIMS P2 Q6

Secondary 4
6 marks
2025 School of Science and Technology Prelims A Math Paper 2

The expression \(3 \cos \theta + 5 \sin \theta\) is defined for \(0 \leq \theta \leq \frac{\pi}{2}\) radians.

  1. Express \(3 \cos \theta + 5 \sin \theta\) in the form \(R \cos(\theta - \alpha)\), where \(R > 0\) and \(\alpha\) is an acute angle in radian.[2]
  2. Hence, solve the equation \(3 \cos \theta + 5 \sin \theta = 4\),[2]
  3. find the minimum value of \(\frac{1}{(3 \cos \theta + 5 \sin \theta)^2 + 1}\).[2]

Solution:

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Answer:(i) \(\sqrt{34}\cos\left(\theta-\tan^{-1}\!\left(\frac{5}{3}\right)\right)\) (ii) \(\theta=0.216\text{ rad}\) (iii) \(\frac{1}{35}\)

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