Answer
$Amplitude = \frac{4}{3}$
$Period = \frac{2\pi}{3}$
$Horizontal\ shift = \frac{\pi}{3}$ i.e right shift $\frac{\pi}{3}$
$Vertical\ shift = \frac{2}{3}$ ($\frac{2}{3}$ units shift upward)
$Phase = -\pi$
Work Step by Step
If C is any real number and $B> 0$, then the graphs of $y = k + A\sin(Bx+C)$ and $y = k + A\cos (Bx+C)$ will have
$Amplitude = |A|$
$Period = \frac{2\pi}{B}$
$Horizontal\ shift = –\frac{C}{B}$
$Vertical\ shift = k$
$Phase = C$
so for $y = \frac{2}{3} - \frac{4}{3}\cos (3x - \pi )$
$Amplitude = |-\frac{4}{3}| = \frac{4}{3}$
$Period = \frac{2\pi}{3}$
$Horizontal\ shift = (–\frac{-\pi}{3}) = \frac{\pi}{3}$ i.e right shift $\frac{\pi}{3}$
$Vertical\ shift = \frac{2}{3}$ ($\frac{2}{3}$ units shift upward)
$Phase = -\pi$
