[填空题]
The mean depth, D, in metres, of a mountain lak1 *t)e n)id;m:b +yp,ifea(ym nslsa( e fluctuatef 4g(w20wnlb- )upd whs in a yearly cycle and can b(wpf2nw hu)gw 0b4d l-e modelled by the function
D(t)=acos(kt)+b,where t is the elapsed time, in months, since the beginning of an autumn season.
The mean depth of the lake on month 11 is 33.2 m and on month 5 is 22.8 m.
1.Find the value of k, in degrees. $^{\circ}$
2.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. a ≈ b ≈
3.Hence find the mean depth of the lake on month 8. m
4.Draw the graph of y=D(t) on the grid below, for one full year, indicating clearly the minimum and maximum points.
