Question

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

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:

$\frac{2\pi}{b}$

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

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

So our period is $\frac{2\pi}{3}$

Our phase shift is by $\frac{\pi}{6}$ units to the right

and our amplitude is 3.