2026 ASRJC P1 Q3

2026 ASRJC P1 Q3

Junior College 2
5 marks

A curve \(C\) has parametric equations \[x=\sin t,\qquad y=\cos2t,\qquad \frac\pi2<t<\frac{3\pi}{2},\quad t\ne\pi.\]

  1. Find the equation of the normal at the point \(P(\sin p,\cos2p)\).[2]
  2. The normal at \(P\) passes through another distinct point \(Q(\sin q,\cos2q)\). Show that \(8\sin p(\sin p+\sin q)=-1\).[3]

Solution:

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Answer:(a) \(y-\cos2p=\frac{x-\sin p}{4\sin p}\) (b) \(8\sin p(\sin p+\sin q)=-1\)

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