IB Math HL Trigonometry Test 2 2013 P1 Q6

IB Math HL Trigonometry Test 2 2013 P1 Q6

IB Year 6 | Grade 12
9 marks

Consider \(f(x)=-3\sin(\pi x)+p\). The maximum value is \(5\).

  1. Find \(p\) and the range of \(f\).[2]
  2. Sketch \(f\) for \(0\le x\le5\).[3]
  3. Solve \(f(x)=2\) for \(0\le x\le5\).[2]
  4. Find the coordinates of the local maximum points of \(f\).[2]

Solution:

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Answer:(a) \(p=2\), range \([-1,5]\). (c) \(x=0,1,2,3,4,5\). (d) \((1.5,5)\), \((3.5,5)\).

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