### Instruction: Find the phase shift of the graph of $y = \sin (3x - \pi).$.### Response: I recall that the phase shift of a trigonometric function is the horizontal displacement of its graph from the standard position.
For example, the graph of $y = \sin x$ has no phase shift, and it starts at the origin and repeats every $2\pi$ units.
The graph of $y = \sin (x - \pi/2)$ has a phase shift of $\pi/2$ units to the right, and it starts at the point $(\pi/2, 1)$ and repeats every $2\pi$ units.
To find the phase shift of a function of the form $y = \sin (ax + b)$, I can use the formula $-\frac{b}{a}$, where $a$ is the coefficient of $x$ and $b$ is the constant term.
In this case, $a = 3$ and $b = -\pi$, so the phase shift is $-\frac{-\pi}{3} = \frac{\pi}{3}$ units to the right.
Alternatively, I can think of the function as $y = \sin (3x - \pi) = \sin (3(x - \pi/3))$, and see that it is the graph of $y = \sin 3x$ shifted $\pi/3$ units to the right.
Either way, I get the same answer.