Find the value of a .

(i)     Show that the period of f is $\pi$ .

(ii)    Hence, find the value of b .

Given that $0 < c < \pi$  , write down the value of c .

evidence of valid approach     (M1)

e.g. $\frac{{{\text{max }}y{\text{ value}} - {\text{min }}y{\text{ value}}}}{2}$ , distance from $y = - 1$

$a = 3$     A1     N2

[2 marks]

(i) evidence of valid approach     (M1)

e.g. finding difference in x-coordinates, $\frac{\pi }{2}$

evidence of doubling     A1

e.g. $2 \times \left( {\frac{\pi }{2}} \right)$

${\text{period}} = \pi$      AG     N0

(ii) evidence of valid approach     (M1)

e.g. $b = \frac{{2\pi }}{\pi }$

$b = 2$     A1     N2

[4 marks]

$c = \frac{\pi }{4}$     A1     N1

[1 mark]

A pleasing number of candidates correctly found the values of a, b, and c for this sinusoidal graph.

A pleasing number of candidates correctly found the values of a, b, and c for this sinusoidal graph. Some candidates had trouble showing that the period was $\pi$ , either incorrectly adding the given $\pi /4$ and $3\pi /4$ or using the value of b that they found first for part (b)(ii).

A pleasing number of candidates correctly found the values of a, b, and c for this sinusoidal graph. Some candidates had trouble showing that the period was $\pi$ , either incorrectly adding the given $\pi /4$ and $\pi /3$ or using the value of b that they found first for part (b)(ii).