How do you find the amplitude and period for the function #y=5cos4theta#?

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Answer 1 · 2018-05-06T12:26:00

Please see the explanation below

The amplitude of #cosx# is #=1#

Therefore,

the amplitude of #5costheta# is #=5#

For a periodic function

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

where #T# is the period

Therefore,

#5cos4theta=5cos4(theta+T)#

#=5(cos(4theta+4T))#

#=5(cos4thetacos4T-sin4thetasin4T)#

Comparing the #LHS# and the #RHS#

#{(cos4T=1),(sin4T=0):}#

#=>#, #4T=2pi#

#T=pi/2#

The period is #=pi/2#

graph{5cos(4x) [-12.66, 12.66, -6.33, 6.33]}