Question

Given the cosine equation y = 2cos(4x) - 1, What is the midline?

Answer 1

`y = 2 \cos(4x) - 1 \\ when \: y = 0 \\ \cos(4x) = (1)/(2) \\ 4x = 60 \\ x = 15 \\ when \: x = 0 \\ y = 2 - 1 = 1 \\ intercepts = > (15, \: 0) \: and \: (0, \: 1) \\ midpoints : ( (15 + 0)/(2) , \: (0 + 1)/(2) ) \\ = (7.5, \: 0.5) \\ gradient = (1 - 0)/(0 - 15) \\ = - (1)/(15) \\ y = mx + c \\ at \: (7.5, \: 0.5) \\ 0.5 = - (1)/(15) * 7.5 + c \\ 0.5 = - 0.5 + c \\ c = 1 \\ \therefore \: y = - (1)/(15) x + 1 \\ = > 15y = - x + 15`