### Instruction: Find the phase shift of the graph of $y = \sin (3x - \pi).$.### Response: I know that the standard form of a sine function is $y = a \sin (b(x - h)) + k,$ where $a$ is the amplitude, $b$ is the frequency, $h$ is the horizontal shift or phase shift, and $k$ is the vertical shift.
So I want to write $y = \sin (3x - \pi)$ in that form by factoring out a $3$ from the argument of the sine function.
I get $y = \sin (3(x - \pi/3)),$ which is almost in the standard form, except for a missing $a$ and $k.$
But I can just assume that $a = 1$ and $k = 0,$ since they do not affect the phase shift.
Now I can compare my equation with the standard form and see that $h = \pi/3,$ which means the phase shift is $\pi/3$ units to the right.