Sketch the graph of \(y = \left| {\cos \left( {\frac{x}{4}} \right)} \right|\) for \(0 \leqslant x \leqslant 8\pi \).

Solve \(\left| {\cos \left( {\frac{x}{4}} \right)} \right| = \frac{1}{2}\) for \(0 \leqslant x \leqslant 8\pi \).

    A1A1

Note:     Award A1 for correct shape and A1 for correct domain and range.

[2 marks]

\(\left| {\cos \left( {\frac{x}{4}} \right)} \right| = \frac{1}{2}\)

\(x = \frac{{4\pi }}{3}\)     A1

attempting to find any other solutions     M1

Note:     Award (M1) if at least one of the other solutions is correct (in radians or degrees) or clear use of symmetry is seen.

\(x = 8\pi  - \frac{{4\pi }}{3} = \frac{{20 \pi }}{3}\)

\(x = 4\pi  - \frac{{4\pi }}{3} = \frac{{8\pi }}{3}\)

\(x = 4\pi  + \frac{{4\pi }}{3} = \frac{{16\pi }}{3}\)     A1

Note:     Award A1 for all other three solutions correct and no extra solutions.

Note:     If working in degrees, then max A0M1A0.

[3 marks]