Please write down all your work. Thank you.

16. Let f(t) = a cosb(t - c) + d , t 2 0. Part of the graph of y = f() is given below. y When t = 3 , there is a maximum value of 29, at M. 301 M 27 When t = 9 , there is a minimum value of 15. 24 21/ 16a. [7 marks] 18 (i) Find the value of a. 15 (ii) Show that 6 12- (iii) Find the value of d. 9 (iv) Write down a value for c. 2 3 5 6 7 8 9 10 1 16b. [2 marks] The transformation P is given by a horizontal stretch of a scale factor of 2 , followed by a translation of Let M' be the image of M under P. Find the coordinates of M' 16c. [4 marks] The graph of g is the image of the graph of funder P. Find 9(t) in the form 9(t) = 7 cos B(t - c) + D 16d. [3 marks] The graph of g is the image of the graph of funder P. Give a full geometric description of the transformation that maps the graph of g to the graph of f