How do you find the amplitude and period of #y= 2 - 3 cos pi•x#?

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Answer 1 · 2018-07-07T06:13:17

The amplitude is #=5#. The period is #=2#

The amplitude of #cosx# is

#-1<=cosx<=1#

Multiply by #-3#

#3>=-3cosx>=-3#

Add #2

#2+3>=(2-3cosx)>=2-3#

#5>=(2-3cosx)>=-1#

#-1<=(2-3cosx)<=5#

The period #T# of a periodic function #f(x)# is

#f(x)=f(x+T)#

Therefore,

#(2-3cospix)=2-3cospi(x+T)#

#=>#, #-3cos(pix)=-3cos(pix+piT)#

#=>#, #cos(pix)=cos(pix)cos(piT)-sin(pix)sin(piT)#

Comparing both sides of the equation

#{ (cospiT=1),(sinpiT=0):} #

#<=>#, #piT=2pi#

#=>#, #T=2#

The period is #=2#

graph{2-3cos(pix) [-10.03, 12.465, -2.81, 8.435]}