6. The mean depth, D, in metres, of a mountain lake fluctuates in a yearly cycle and can be modelled by the function D(t) = acos (kt) +b, where f is the elapsed time, in months, since the beginning of an autumn season. The mean depth of the lake on month 1 is 33.2 ur and on month 5 is 22.8 m. (a) Find the value of &, in degrees. (b) Set up a pair of equations and find the value of a and the value of b. Give your answers correct to the nearest integer. 3 (c) Hence find the mean depth of the lake on month 8. 2 (d) Draw the graph of y = D(t) on the grid below, for one full year, indicating clearly the minimum and maximum points