What is the period and amplitude for #f(x) = 2cos(4x + pi) -1#?

1 Answer
Gió
May 15, 2015

You have the form:
#y=#Amplitude#*cos((2pi)/(period)x+....)#
So in your case:
Amplitude=#2#
Period=#(2pi)/4=pi/2#

#+pi# is an initial phase and #-1# is a vertical shift.

Graphically:
graph{2cos(4x+pi)-1 [-10, 10, -5, 5]}

Note that your #cos# is displaced downwards and now oscillates around #y=-1#! It also starts at #-1# as #cos(0+pi)#.

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