How do you write an equation of the cosine function with amplitude 3 and period 4π?

2 Answers
Dean R.
May 28, 2018

#y = 3 cos({2pi}/{4pi} x) = 3 cos(x/2) #

Douglas K.
May 28, 2018

The general form for the cosine function is:

#y = Acos(Bx+C)+D#

The amplitude is: #|A|#

The period is: #P = (2pi)/B#

The phase shift is #phi=-C/B#

The vertical shift is D

Explanation:

Given:

The amplitude is 3:

#|A| = 3#

The above implies that A could be either positive or negative but we always choose the positive value because the negative value introduces a phase shift:

#A = 3#

Given:

The period is

#P = 4pi#

#4pi = (2pi)/B#

#B = 1/2#

Nothing is said about the phase shift and the vertical shift, therefore, we shall assume that #C# and #D# are 0.

Substitute these values into the general form:

#y = 3cos(1/2x)#

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