(Solved): The height of water, in metres, in Dungeness harbour is modelled by the function H(t)=asin(b(tc ...

The height of water, in metres, in Dungeness harbour is modelled by the function H(t)=asin(b(t?c))+d, where t is the number of hours after midnight, and a,b,c and d are constants, where a>0,b>0 and c>0. The following graph shows the height of the water for 13 hours, starting at midnight. The first high tide occurs at 04:30 and the next high tide occurs 12 hours later. Throughout the day, the height of the water fluctuates between 2.2 m and 6.8 m. All heights are given correct to one decimal place. (a) Show that b=6??. (b) Find the value of a. (c) Find the value of d. (d) Find the smallest possible value of c. (e) Find the height of the water at 12:00. (f) Determine the number of hours, over a 24-hour period, for which the tide is higher than 5 metres.