2026 CCHY P1 Q14

2026 CCHY P1 Q14

Secondary 4
6 marks

The function \(g\) is defined by \(g(x)=-5\sin\dfrac{3x}2-1\) for all values of \(x\).

  1. Write down the amplitude and period of \(g(x)\).[2]
  2. On the axes, sketch the graph of \(y=g(x)\), for \(-180^\circ\le x\le180^\circ\).[3]
  1. State the range of values of \(m\) such that the equation \(-5\sin\dfrac{3x}2-1=m\) has no solution.[1]

Solution:

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Answer:(a) Amplitude 5; period \(240^\circ\). (b) See graph. (c) \(m<-6\) or \(m>4\).

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