Sketching a sine curve and the related cosecant curve, then solving a modulus equation

Sketching a sine curve and the related cosecant curve, then solving a modulus equation

IB Year 6 | Grade 12
7 marks

The function \(\mathrm{f}\) is given by \(\mathrm{f}(x)=2\,\mathrm{cosec}\,3x\).

  1. On the grid below, sketch the graph of \(y=\sin3x\) for \(0\le x\le\pi\).[2]
  2. On the same axes, sketch the graph of \(y=\mathrm{f}(x)\) for \(0<x<\pi\), showing every vertical asymptote.[3]
  3. Solve the equation \(\left|\mathrm{f}(x)\right|=4\) for \(0<x<\pi\).[2]

Solution:

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Answer:(b) asymptotes \(x=0,\ x=\dfrac{\pi}{3},\ x=\dfrac{2\pi}{3},\ x=\pi\) (c) \(x=\dfrac{\pi}{18},\ \dfrac{5\pi}{18},\ \dfrac{7\pi}{18},\ \dfrac{11\pi}{18},\ \dfrac{13\pi}{18},\ \dfrac{17\pi}{18}\)

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