How do you find the phase shift of a trigonometric function?

The phase shift of a graph determines if the graph is going to be shifted left or right on the x-plane of the graph.


From the example above the phase shift of the graph would be.


Let's do a short example of how the phase shifts would happen to a basic sin(x) function.


Basic Sin Function

If you take the function and shift it to the left $\frac{\pi}{2}$ length.


Shifted Left

You can also go the other way and shift it to the right $\frac{\pi}{2}$ length.


Shifted To the Right

Let's take a look at all three transformations.

All Three Transformations