The road to an island close to the shore is sometimes covered by the tide. When the water rises to the level of the road, the road is closed. On a particular day, the water at high tide is a height 4.6m above mean sea level. The height, h meters, of the tide is modeled by using the equation h = 4.6coskt, where ti s the time in hours from high tide; it is also assumed that high tides occur every 12 hours.

(a) Determine the value of k

The value of k should be 360 / 12 = 30

(b) On the same, a notice says the the road will be closed for 3 hours. Assuming that this notice is correct, find the height of the road above sea level, giving your answer correct to two decimal places.