How do you write an equation of the cosine function with amplitude=3, period = 2pi/3, phase shift = 1pi/9, and vertical shift 4?

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Answer 1 · 2016-11-14T21:58:29

In #y = acos(b(x- c)) + d#:

•#|a|# is the amplitude
•#(2pi)/b# is the period
•#c# is the phase shift
•#d# is the vertical transformation

The amplitude is #3#, so #a= 3#.

The period is #(2pi)/3#, so we solve for #b#.

#(2pi)/b = (2pi)/3#

#b = 3#

The phase shift is #+pi/9#, so #c= pi/9#.

The vertical transformation is #+4#, so #d = 4#.

#:.#The equation is #y = 3cos(3(x- pi/9)) + 4#, which can be written as #y= 3cos(3x - pi/3) + 4#

Hopefully this helps!