### Instruction: Find the phase shift of the graph of $y =  3 \sin \left( x - \frac{\pi}{5} \right).$.### Response: I recall that the general form of a sine function is $y = A \sin (Bx - C) + D$, where $A$ is the amplitude, $B$ is the frequency, $C$ is the horizontal shift, and $D$ is the vertical shift.
I compare this form with the given function and notice that $A = 3$, $B = 1$, $C = \frac{\pi}{5}$, and $D = 0$.
I also remember that the phase shift of a sine function is the amount that the graph is shifted horizontally from the standard sine curve $y = \sin x$.
I see that the phase shift is equal to $C$, but I need to divide it by $B$ to get the correct units of radians.
So, the phase shift is $\frac{C}{B} = \frac{\frac{\pi}{5}}{1} = \frac{\pi}{5}$ radians.
I can check my answer by graphing both functions and seeing that they match up after shifting the standard sine curve to the right by $\frac{\pi}{5}$ radians.