What is the period and amplitude for #y=cos9x#?

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Answer 1 · 2018-07-01T11:48:27

The period is #=2/9pi# and the amplitude is #=1#

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

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

Here,

#f(x)=cos9x#

Therefore,

#f(x+T)=cos9(x+T)#

#=cos(9x+9T)#

#=cos9xcos9T+sin9xsin9T#

Comparing #f(x)# and #f(x+T)#

#{(cos9T=1),(sin9tT=0):}#

#=>#, #9T=2pi#

#=>#, #T=(2pi)/9#

The amplitude is #=1# as

#-1<=cosx<=1#

graph{cos(9x) [-1.914, 3.56, -0.897, 1.84]}