Corrugated cardboard is produced by gluing corrugated paper between flat sheets of paper. A particular type of corrugated cardboard is made up of two corrugated sheets of paper glued between three flat sheets of paper as shown below. 3 2 Y (4,3) f(x) g(x) x The flat sheets of paper are described by the horizontal lines y = 0, y = 2 and y = 3. The corrugations are described by two functions f(x) and g(x)=-sin(x)+1, where all distances are measured in centimetres. a) Given that f(x) = acos(bx)+c, write down the values of a, b and c. Let d(x) = f(x)- g(x) the vertical distance between the corrugated sheets of paper. The graph of d(x) is plotted below. b) 3 2 1 Y ww 2 6 8 10 12 Show that d(x): 3 1 - + COS 2 2 TTX 2 +sin(x). c) State the period of d(x). d) Determine the maximum and minimum distances between the corrugated paper, correct to three decimal places. 3 e) Find the values of x for which d(x): places. for 1x5. Give non-integer solutions correct to 3 decimal 2