Answer
$Amplitude = |3| = 3$
$Period = \frac{2\pi}{\frac{\pi}{3}} = 6$
$Horizontal\ shift = (–\frac{-\frac{\pi}{3}}{\frac{\pi}{3}}) = 1$
$Phase = -\frac{\pi}{3}$
Work Step by Step
If C is any real number and $B> 0$, then the graphs of $y = A\sin(Bx+C)$ and $y = A\cos (Bx+C)$ will have
$Amplitude = |A|$
$Period = \frac{2\pi}{B}$
$Horizontal\ shift = –\frac{C}{B}$
$Phase = C$
so for $y = 3\cos (\frac{\pi}{3}x - \frac{\pi}{3})$
$Amplitude = |3| = 3$
$Period = \frac{2\pi}{\frac{\pi}{3}} = 6$
$Horizontal\ shift = (–\frac{-\frac{\pi}{3}}{\frac{\pi}{3}}) = 1$
$Phase = -\frac{\pi}{3}$
