College Algebra & Trigonometry, 2018a

418 CHAPTER 9. GRAPHING THE TRIGONOMETRIC FUNCTIONS
Now let’s look at a graph of y = sin(x + π) as compared to the standard graph of
y =sinx.
1
y =sinx
− π 2
0
π
2
π
3π
2
2π
−1
1
y = sin(x + π)
− π 2
0
π
2
π
3π
2
2π
−1
Notice that if we take the standard graph of y = sinx and drag it backwards
along the x-axis a distance of π, we would have the graph of y = sin(x + π).
That’s because each x value is having π added to it, so to arrive at the x value that
produces a particular y-value, we would need to subtract π. Here’s an example:
x + π y = sin(x + π)
0 0
π/2 1
π 0
3π/2 −1
2π 0
In the table above we see the standard x and y values for the graph of the sine
function. In the table below, we add a column that shows the value that x would
need to be for x + π to be the standard values: