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2026 NYGH P2 Q5

2026 NYGH P2 Q5

IP 4
5 marks

The diagram shows the curves \(y=\cos x\) and \(y=\sin2x\) for \(0\leq x\leq\dfrac\pi2\). The two curves intersect at the point \(\left(\dfrac\pi2,0\right)\) and the point \(A\).

  1. Show that the \(x\)-coordinate of \(A\) is \(\dfrac\pi6\).[2]
  2. Find the exact area of the shaded region.[3]

Solution:

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Answer:(a) \(x_A=\dfrac\pi6\) (b) \(\dfrac14\text{ units}^2\)

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