IB Math HL Trigonometry Test 7 2018 P1 Q9

IB Math HL Trigonometry Test 7 2018 P1 Q9

IB Year 6 | Grade 12
9 marks

The graph shows a trigonometric function \(f\) with local maximum \(A(1,8)\) and local minimum \(B(2,-2)\).

  1. Write down[2]
    1. the amplitude of \(f\);
    2. the period of \(f\).
  2. Express \(f(x)\) as \(a\cos(bx)+c\).[4]
  3. Express \(f(x)\) as \(A\sin(Bx+D)+C\), with \(A>0\).[3]

Solution:

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Answer:(a) Amplitude \(5\), period \(2\). (b) \(f(x)=-5\cos(\pi x)+3\). (c) \(f(x)=5\sin(\pi x-\frac{\pi}{2})+3\).

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