Find $\cos \theta$.

Find $\cos 2\theta$.

evidence of valid approach     (M1)

eg$\,\,\,\,\,$right triangle, ${\cos ^2}\theta  = 1 - {\sin ^2}\theta$

correct working     (A1)

eg$\,\,\,\,\,$missing side is 2, $\sqrt {1 - {{\left( {\frac{{\sqrt 5 }}{3}} \right)}^2}}$

$\cos \theta  = \frac{2}{3}$     A1     N2

[3 marks]

correct substitution into formula for $\cos 2\theta$     (A1)

eg$\,\,\,\,\,$$2 \times {\left( {\frac{2}{3}} \right)^2} - 1,{\text{ }}1 - 2{\left( {\frac{{\sqrt 5 }}{3}} \right)^2},{\text{ }}{\left( {\frac{2}{3}} \right)^2} - {\left( {\frac{{\sqrt 5 }}{3}} \right)^2}$

$\cos 2\theta  =  - \frac{1}{9}$    A1     N2

[2 marks]