2026 ZHSS P1 Q10

2026 ZHSS P1 Q10

Secondary 4
8 marks

The equation of a curve is \(y=2\cos^2 3x-\sin4bx+2\), where \(x\) is in radian and \(b\) is a positive constant.

  1. Find, in terms of \(b\), the equation of the normal to this curve at the point \(A(0,4)\).[6]
  2. This normal is parallel to another line \(8y-x=6\). Find the value of \(b\).[2]

Solution:

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Answer:(a) \(y=\dfrac{x}{4b}+4\) (b) \(b=2\)

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