Question

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


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

Answer 1

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.