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