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

1 Answer
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).