College Algebra & Trigonometry, 2018a

402 CHAPTER 9. GRAPHING THE TRIGONOMETRIC FUNCTIONS
In the previous table we can see that the function y = sin(2x) completes one full
cycle between 0 and π radians instead of the the standard 0 to 2π radians. The
graph for these points is shown below. The coordinates for the x-values between
π and 2π radians are shown as well.
1
1
2
0 30 60 90 120 150 180 210 240 270 300 330 360
− 1 2
−1
In this graph, you can see that there are two complete waves between 0 and 2π
radians, or one complete wave between 0 and π radians. So, in a sine or cosine
function of the form y = A sin Bx, the amplitude will be |A| and the period will
be 2π B
. The standard graph for one complete cycle of the function y = sin(2x) is
shown below:
1
0
π
4
π
2
3π
4
π
−1
Notice that, because the period has been cut in half, the x-coordinates that correspond
to the maximum, minimum, and zero y-coordinates are cut in half as