2025 PHS P2 Q5

2025 PHS P2 Q5

Secondary 4
8 marks
  1. Express \(6\sin t+8\cos t\) in the form \(R\sin(t+\alpha)\), where \(R>0\) and \(0<\alpha<\dfrac\pi2\).[3]
  2. An electric voltage from a battery, \(V\) volts varies with time and is given by \(V=6\sin t+8\cos t\), where \(t\) is the time in milliseconds.
    1. An electrical drill requires a voltage exceeding 10 volts to work. Determine if the electrical drill can be used with the battery.[2]
    2. Find the value of \(t\) when the electric voltage is 4 volts at the first instant.[3]

Solution:

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Answer:(a) \(10\sin(t+\tan^{-1}(4/3))\). (b)(i) No; maximum 10 V. (ii) \(1.80\text{ ms}\).

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