College Algebra & Trigonometry, 2018a

9.4. PHASE SHIFT 419
x x + π y = sin(x + π)
−π 0 0
−π/2 π/2 1
0 π 0
π/2 3π/2 −1
π 2π 0
Here’s a graph of these values:
1
−π − π 2
0
π
2
π
−1
y = sin(x + π)
This is the same graph of y = sin(x + π) that we saw on the previous page,
but anchored to different points on the x-axis. Either graph would be a correct
response to a question asking for at least one period of the graph of y = sin(x+π).
Let’s look at another example:
Example 2
Graph at least one period of the given function: y = sin(x+ π 3 ).
Be sure to indicate important points along the x and y axes.
In this simplified example, we really have only one transformation to worry
about - the phase shift. Notice that the amplitude, period and vertical shift have
all been left out. When considering a sine or cosine graph that has a phase shift, a
good way to start the graph of the function is to determine the new starting point
of the graph. In the previous example, we saw how the function y = sin(x + π)