IB Math HL Trigonometry Test 5 2016 P1 Q2

IB Math HL Trigonometry Test 5 2016 P1 Q2

IB Year 6 | Grade 12
8 marks

The graph of \(f(x)=a\cos(bx)+c\) for \(-5\le x\le14\) is shown. It has a minimum at \((0,-3)\) and a maximum at \((4,7)\).

  1. Find \(a,b,c\).[4]
  2. The function can be written as \(f(x)=-a\sin(bx-d)+c\), where \(a,b,c\) are as above. Find the smallest positive value of \(d\).[2]
  3. Solve \(f(x)+3=0\) for \(-5\le x\le14\).[2]

Solution:

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Answer:(a) \(a=-5,b=\frac{\pi}{4},c=2\). (b) \(d=\frac{\pi}{2}\). (c) \(x=0,8\).

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