IB Math HL Trigonometry Test 1 2012 P1 Q6

IB Math HL Trigonometry Test 1 2012 P1 Q6

IB Year 6 | Grade 12
8 marks

Consider \(f(x)=2\sec4x\).

  1. Sketch \(y=f(x)\) for \(0\le x\le\pi\), indicating clearly the equations of all asymptotes.[4]
  2. Write down the smallest positive solution of \(f(x)=-2\).[2]
  3. Find the number of solutions of \(|f(x)|=3\) for \(0\le x\le\pi\).[2]

Solution:

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Answer:(a) Asymptotes \(x=\frac{\pi}{8},\frac{3\pi}{8},\frac{5\pi}{8},\frac{7\pi}{8}\). (b) \(\frac{\pi}{4}\). (c) \(8\) solutions.

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