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Find the amplitude, period, and phase shift of the function.


y=3 cos(3x-(\pi)/(2))+1
Give the exact values, not decimal approximations.

User Marinos
by
8.2k points

1 Answer

1 vote

Cosine is transformed in the form:


f(x)=a\cos(b(x-c))+d

The amplitude is a

The period of cosine is:


(2\pi)/(b)

And the phase shift is always by c, so that means our transformed functon in the form mentioned above looks like:


f(x)=3\cos{(3(x-(\pi)/(6)}))+1

So our period is
(2\pi)/(3)

Our phase shift is by
(\pi)/(6) units to the right

and our amplitude is 3.

User Dalton Pereira
by
8.0k points
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