Graph f (x) = 3cos (4pix -pi/2) -2

Answer 1

f (x) = 3cos (4pix -pi/2) -2
= 3cos (4π(x - 1/8) ) - 2 <---- a horizontal shift of 1/8 to right

period = 2π/(4π) = 1/2

On the x-axis mark off 0, 1/8, 2/8, 3/8 and 4/8

the magnitude of your cosine curve is 3, so on the y-axis, mark off 5 or 6 units above and below

Knowing the general shape of a cosine curve, plot
(0,3), (1/8, 0) , (2/8,-1), (3/8,0) and (4/8, 3)

now move that curve 1/8 units to the right, then 2 units down
http://www.wolframalpha.com/input/?i=plot+y+%3D+3cos+(4%CF%80x)+,+y+%3D+3cos+(4pix+-pi%2F2)+-2,+y+%3D+3cos+(4%CF%80(x+-+1%2F8)+)+-+2

notice the first graph establishes the shape.
the second equation is as stated
the third equation in my simplied version
note that the 2nd and third graphs coincide.