How do you graph and list the amplitude, period, phase shift for #y=1/2cosx+5/2#?

1 Answer
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Sep 22, 2016

Amplitude #1/2#, period#=2pi# and phase shift#=0# (none).

Explanation:

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

#A=# amplitude
#(2pi)/absB=# period
#C/B=# phase shift
#D=# vertical shift

For the equation #y=1/2cosx+5/2#
#A=1/2#, #B=1#, #C=0#, #D=5/2#
Amplitude = #1/2#
Period=#(2pi)/abs1=2pi# (the "regular" period of cosine)
Phase shift = #0/1 =0# (no phase shift)
Vertical shift =#5/2# (up #5/2#)

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