How do you graph and list the amplitude, period, phase shift for #y=-3cos(3x)+3#?

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Answer 1 · 2018-02-02T02:36:49

The amplitude of the function is #3#, the period is #(2pi)/3#, and the phase shift is #0#.

For the general #cos# wave

#y=Acos(B(x-C))+D#,

the wave is amplified by #|A|#, horizontally compressed by #B#, translated right #C# (phase shift), and translated up #D#.

Here are the values of our equation:

#y=-3cos(3x)+3#

#|A|="amplitude"=3#

#B="compression"=3#

#C="phase shift"=0#

#D="vertical shift"=3#

To find our period, we take #2pi# (the period of the normal sinusoidal wave) and divide it by our B value:

#"period"=(2pi)/B=(2pi)/3#

Finally, the phase shift is our #C# value, which in this case is #0# (because it is not present).