IB Math HL Trigonometry Test 5 2016 P2 Q3

IB Math HL Trigonometry Test 5 2016 P2 Q3

IB Year 6 | Grade 12
9 marks

Let \(f(x)=6\sin(\pi x)+8\cos(\pi x)+15\).

  1. Find the period and range of \(f\).[3]
  2. Express \(f\) as \(a\cos(b(x-d))+c\), where \(a,b,c,d\) are positive real numbers.[4]
  3. Solve \(f(x)\ge x^2\).[2]

Solution:

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Answer:(a) Period \(2\), range \([5,25]\). (b) \(a=10,b=\pi,c=15,d=\frac1\pi\arctan\frac34\). (c) \([-4.21,-3.12]\cup[-2.60,2.93]\cup[3.65,4.52]\).

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