IB Math HL Trigonometry Test 2 2013 P2 Q5

IB Math HL Trigonometry Test 2 2013 P2 Q5

IB Year 6 | Grade 12
6 marks

Let \(f(x)=\tan^3x\).

  1. Find the exact solutions of \(f(x)=-3\sqrt3\) for \(-\pi\le x\le2\pi\).[4]
  2. Hence solve \(f(2x)=-3\sqrt3\) for \(-\frac{\pi}{2}\le x\le\pi\).[2]

Solution:

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Answer:(a) \(x=-\frac{\pi}{3},\frac{2\pi}{3},\frac{5\pi}{3}\). (b) \(x=-\frac{\pi}{6},\frac{\pi}{3},\frac{5\pi}{6}\).

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