Find the value of

(i)     $A$;

(ii)     $B$;

(iii)     $C$.

Solve $f(x) = 3$ for $0 \le x \le \pi$.

(i)     $A =  - 3$     A1

(ii)     period $= \frac{\pi }{B}$     (M1)

$B = 2$     A1

Note:     Award as above for $A = 3$ and $B =  - 2$.

(iii)     $C = 2$     A1

[4 marks]

$x = 1.74,{\text{ }}2.97\;\;\;\left( {x = \frac{1}{2}\left( {\pi  + \arcsin \frac{1}{3}} \right),{\text{ }}\frac{1}{2}\left( {2\pi  - \arcsin \frac{1}{3}} \right)} \right)$     (M1)A1

Note:     Award (M1)A0 if extra correct solutions eg $( - 1.40,{\text{ }} - 0.170)$ are given outside the domain $0 \le x \le \pi$. Do not award FT in (b).

[2 marks]

Total [6 marks]