Graph of the modulus of a secant drawn from its cosine, with asymptotes and an equation

Graph of the modulus of a secant drawn from its cosine, with asymptotes and an equation

IB Year 6 | Grade 12
8 marks

The function \(\mathrm{f}\) is given by \(\mathrm{f}(x)=\left|\sec\left(\frac{\pi x}{2}\right)\right|\) for \(0\le x\le6\).

  1. Sketch the graph of \(y=\cos\left(\frac{\pi x}{2}\right)\) for \(0\le x\le6\).[3]
  2. On the same diagram, sketch the graph of \(y=\mathrm{f}(x)\), stating the equations of all the vertical asymptotes.[3]
  3. Solve the equation \(\mathrm{f}(x)=2\) for \(0\le x\le6\).[2]

Solution:

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Answer:(b) \(x=1,\ x=3,\ x=5\) (c) \(x=\frac23,\ \frac43,\ \frac83,\ \frac{10}{3},\ \frac{14}{3},\ \frac{16}{3}\)

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