College Algebra & Trigonometry, 2018a

404 CHAPTER 9. GRAPHING THE TRIGONOMETRIC FUNCTIONS
graph to the next is always a “jump” of π 2
along the x-axis. This is one-fourth of
the period: 2π 1
∗ 1 4 = π 2
. So, to determine the labels for the critical values of the
graph along the x-axis, we should take the new period and multiply by 1 4 .
The function we are working with is y = −2sin3x, so to find the new period we
calculated 2π B , which was 2π 3
. Then, in order to label the x-axis properly we
should next take 2π 3 and multiply by 1 4 .
2π
3 ∗ 1 4 = 2π
12 = π 6
So, the critical values along the x-axis will be:
1π
6 , 2π 6 , 3π 6 , and 4π 6
We want to express these in lowest terms, so we would label them as π 6 , π 3 , π 2 , and
2π
3
. The graph will start at zero, then (because the value of the coefficient A is
negative) it will go down to a minimum value at π 6 , back to zero at π 3
, then up to
the maximum at π 2 and back down to zero at 2π 3
to complete one full period of the
graph. The graph for this function is pictured below. Notice that the minimum
y-value is −2 and the maximum y-value is 2 because A =2.
2
1
−1
0
π
6
π
3
π
2
2π
3
−2
y = −2sin3x
Let’s look at an example using the cosine graph.