Part D: Application (14 marks) 1. (a) Show that sin (3x)=3sin x-4sin'x ( b ) Hence, or otherwise, solve the equation sin (3 x )+ sin x=0 for OSX52n (6 marks) P.10 of 11 2. Water tides can be modelled using the function h(t)=asin[ Z (t+3)]+d where h(t) is the height of water at time t (in hours) after midnight. The height of the water at high tide is 14.4 m and the height of the water at low tide is 1.2m. On a particular day, the first high tide occurs at midnight. (a) Using the information given to find the values of a and d. (b ) Sketch the graph of the function. 15 14 13 12 11 10 Nw AUTO 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 0 2 5 (c) If the first high tide occurs at 06:00, how should we modify h(t) ? (8 marks)