Write down the value of $r$.

Find $p$.

Find $q$.

Solve $f(x) = 7$.

$r =  - 4$     A2     N2

Note: Award A1 for $r = 4$.

[2 marks]

evidence of valid approach     (M1)

eg     $\frac{{\max y{\text{ value -- }}y{\text{ value}}}}{2}$, distance from $y = 10$

$p = 8$     A1     N2

[2 marks]

valid approach     (M1)

eg     period is $24$, $\frac{{360}}{{24}}$, substitute a point into their $f(x)$

$q = \frac{{2\pi }}{{24}}\left( {\frac{\pi }{{12}},{\text{ exact}}} \right)$, $0.262$ (do not accept degrees)     A1     N2

[2 marks]

valid approach     (M1)

eg     line on graph at $y = 7,{\text{ }}8\cos \left( {\frac{{2\pi }}{{24}}(x - 4)} \right) + 10 = 7$

$x = 11.46828$

$x = 11.5$   (accept $(11.5, 7)$)     A1     N2

[2 marks]

Note: Do not award the final A1 if additional values are given. If an incorrect value of $q$ leads to multiple solutions, award the final A1 only if all solutions within the domain are given.