How do you write an equation of the cosine function with amplitude of 2, period of 2π/3, phase shift of π/6, and a vertical shift of 1?

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Answer 1 · 2016-09-17T03:38:42

#y=2cos(3x-pi/2)+1#

The general equation of cosine is #y=Acos(Bx-C)+D#,
where
#A=# the amplitude

#(2pi)/absB=# the period

#C/B=# the phase shift

#D=# the vertical shift

In this example, the amplitude is given as 2, the period #(2pi)/3#, the phase shift is #pi/6#, and vertical shift is 1.

#A=2#

#(2pi)/3=(2pi)/absB# so #B=3#

#pi/6=C/B=C/3#

#pi/6=C/3# so #C=pi/2#

#D=1#

Giving us the equation

#y=2cos(3x-pi/2)+1#