Solve the equation $3{\cos ^2}x - 8\cos x + 4 = 0$, where $0 \leqslant x \leqslant 180^\circ$, expressing your answer(s) to the nearest degree.

Find the exact values of $\sec x$ satisfying the equation $3{\sec ^4}x - 8{\sec ^2}x + 4 = 0$.

attempting to solve for $\cos x$ or for u where $u = \cos x$ or for x graphically.     (M1)

EITHER

$\cos x = \frac{2}{3}{\text{ (and 2)}}$     (A1)

OR

$x = 48.1897 \ldots ^\circ$     (A1)

THEN

$x = 48^\circ$     A1

Note: Award (M1)(A1)A0 for $x = 48^\circ ,{\text{ }}132^\circ$.

Note: Award (M1)(A1)A0 for 0.841 radians.

[3 marks]

attempting to solve for $\sec x$ or for $v$ where $v = \sec x$.     (M1)

$\sec x = \pm \sqrt 2 {\text{ }}\left( {{\text{and }} \pm \sqrt {\frac{2}{3}} } \right)$     (A1)

$\sec x = \pm \sqrt 2$     A1

[3 marks]

Part (a) was generally well done. Some candidates did not follow instructions and express their final answer correct to the nearest degree. A large number of candidates successfully employed a graphical approach.

Part (b) was not well done. Common errors included attempting to solve for x rather than for $\sec x$, either omitting or not considering $\sec x =  - \sqrt 2$, not rejecting $\sec x =  \pm \sqrt {\frac{2}{3}}$ and not working with exact values.