2023 YTSS P1 Q13

2023 YTSS P1 Q13

Secondary 4
8 marks
  1. Write \(\sqrt3\cos\theta+\sin\theta\) in the form \(R\cos(\theta-\alpha)\) where \(R>0\) and \(0<\alpha<\dfrac\pi2\) radians.[3]
  2. Find the minimum value of \(\sqrt3\cos\theta+\sin\theta\) and the corresponding value of \(\theta\).[2]
  3. Solve the equation \(\sqrt3\cos\theta+\sin\theta=-1\) for \(0<\theta<2\pi\).[3]

Solution:

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Answer:(a) \(2\cos(\theta-\dfrac\pi6)\). (b) \(-2\) at \(\theta=\dfrac{7\pi}6\) (mod \(2\pi\)). (c) \(\dfrac{5\pi}6,\dfrac{3\pi}2\).

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