### Instruction: Find the phase shift of the graph of $y = \sin (3x - \pi).$.### Response: I know that the graph of $y = \sin x$ is a sinusoidal curve that repeats every $2\pi$ radians, and has a maximum value of $1$ and a minimum value of $-1$ at $x = \pi/2$ and $x = -\pi/2$, respectively.
I also know that if I have a function of the form $y = \sin (kx + b)$, where $k$ and $b$ are constants, then $k$ affects the period of the function and $b$ affects the phase shift of the function.
The period of the function is the smallest positive value of $x$ such that $y = \sin (kx + b)$ repeats itself.
It is given by the formula $P = 2\pi/k$.
The phase shift of the function is the horizontal displacement of the graph from the standard $y = \sin x$ curve.
It is given by the formula $\phi = -b/k$.
In this problem, I have $k = 3$ and $b = -\pi$, so I can plug these values into the formulas for the period and the phase shift.
The period is $P = 2\pi/3$, which means that the graph repeats itself every $2\pi/3$ radians, or every $120$ degrees.
The phase shift is $\phi = -(-\pi)/3 = \pi/3$, which means that the graph is shifted to the right by $\pi/3$ radians, or $60$ degrees, from the standard $y = \sin x$ curve.
Therefore, the phase shift of the graph of $y = \sin (3x - \pi)$ is $\pi/3$ radians, or $60$ degrees.