find the value of \(\cos x;\)

find the value of \(\cos 2x.\)

valid approach     (M1)

eg\(\;\;\;\), \({\sin ^2}x + {\cos ^2}x = 1\)

correct working     (A1)

eg\(\;\;\;{4^2} - {3^2},{\text{ }}{\cos ^2}x = 1 - {\left( {\frac{3}{4}} \right)^2}\)

correct calculation     (A1)

eg\(\;\;\;\frac{{\sqrt 7 }}{4},{\text{ }}{\cos ^2}x = \frac{7}{{16}}\)

\(\cos x =  - \frac{{\sqrt 7 }}{4}\)     A1     N3

[4 marks]

correct substitution (accept missing minus with cos)     (A1)

eg\(\;\;\;1 - 2{\left( {\frac{3}{4}} \right)^2},{\text{ }}2{\left( { - \frac{{\sqrt 7 }}{4}} \right)^2} - 1,{\text{ }}{\left( {\frac{{\sqrt 7 }}{4}} \right)^2} - {\left( {\frac{3}{4}} \right)^2}\)

correct working     A1

eg\(\;\;\;2\left( {\frac{7}{{16}}} \right) - 1,{\text{ }}1 - \frac{{18}}{{16}},{\text{ }}\frac{7}{{16}} - \frac{9}{{16}}\)

\(\cos 2x =  - \frac{2}{{16}}\;\;\;\left( { =  - \frac{1}{8}} \right)\)     A1     N2

[3 marks]

Total [7 marks]

Many candidates were able to find the cosine ratio of \(\frac{{\sqrt 7 }}{4}\) but did not take into account the information about the obtuse angle and seldom selected the negative answer. Finding \(\cos 2x\) proved easier; the most common error seen was \(\cos 2x = 2\cos x\).

Many candidates were able to find the cosine ratio of \(\frac{{\sqrt 7 }}{4}\) but did not take into account the information about the obtuse angle and seldom selected the negative answer. Finding \(\cos 2x\) proved easier; the most common error seen was \(\cos 2x = 2\cos x\).