The diagram shows part of the curve with equationy=f(x) , where f(x)=1+2sin(px°+q°) ,pandqbeing positive constants andq≤ 90. The curve cuts they-axis at the pointAand thex-axis at the pointsCandD. The pointBis a maximum point on the curve.

Given that the coordinates ofAandCare (0, 2) and (45, 0) respectively:

(a) Calculate the value ofq.

(b) Show thatp=4.

(c) Find the coordinates ofBandD.

I can do question a, but I am really stuck on b and c.