Find the phase shift of the graph of $y =  3 \sin \left( x - \frac{\pi}{5} \right).$
Since the graph of $y = 3 \sin \left( x - \frac{\pi}{5} \right)$ is the same as the graph of $y = 3 \sin x$ shifted $\frac{\pi}{5}$ units to the right, the phase shift is $\boxed{\frac{\pi}{5}}.$

[asy]import TrigMacros;

size(400);

real g(real x)
{
	return 3*sin(x - pi/5);
}

real f(real x)
{
	return 3*sin(x);
}

draw(graph(g,-3*pi,3*pi,n=700,join=operator ..),red);
draw(graph(f,-3*pi,3*pi,n=700,join=operator ..));
trig_axes(-3*pi,3*pi,-4,4,pi/2,1);
layer();
rm_trig_labels(-5, 5, 2);
[/asy]
\frac{\pi}{5}
Level 1
Precalculus
Problem: Find the phase shift of the graph of $y =  3 \sin \left( x - \frac{\pi}{5} \right).$
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the phase shift of the sine function, we need to understand the general form of the sine function, which is given by $y = a \sin(b(x - c)) + d$. In this form, $c$ represents the phase shift. 

In the given function $y = 3 \sin \left( x - \frac{\pi}{5} \right)$, we can identify the components: the amplitude $a$ is 3, the coefficient of $x$ is 1 (which means $b = 1$), and the term $(x - \frac{\pi}{5})$ indicates a horizontal shift. 

The phase shift is determined by the value of $c$ in the expression $(x - c)$. Here, $c$ is $\frac{\pi}{5}$. The phase shift is calculated as the value of $c$ itself, which indicates how much the graph is shifted to the right. 

Since the sine function normally starts at the origin (0,0) for $y = \sin(x)$, the presence of $(x - \frac{\pi}{5})$ means the entire graph is shifted to the right by $\frac{\pi}{5}$. 

Thus, the final answer for the phase shift is $\frac{\pi}{5}$.<|END_OF_LATENT|> The final answer is $\frac{\pi}{5}$.