IB Math HL Trigonometry Test 7 2018 P1 Q4

IB Math HL Trigonometry Test 7 2018 P1 Q4

IB Year 6 | Grade 12
14 marks

Consider \(f(x)=3\sin6x+5\) for \(0\le x\le\frac{\pi}{2}\).

  1. Find[3]
    1. the period of \(f\);
    2. the range of \(f\).
  2. Sketch the graph of \(f\) on the diagram.[4]
  3. Solve \(f(x)=8\) in the given interval.[2]
  4. Solve \(f(x)\le5\) in the given interval.[3]
  5. The equation \(f(x)=k\) has exactly two solutions in the interval. Find the possible values of \(k\).[2]

Solution:

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Answer:(a) Period \(\frac{\pi}{3}\), range \([2,8]\). (c) \(x=\frac{\pi}{12},\frac{5\pi}{12}\). (d) \([\frac{\pi}{6},\frac{\pi}{3}]\cup\{0,\frac{\pi}{2}\}\). (e) \(k=8\) or \(2<k<5\).

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