College Algebra & Trigonometry, 2018a

9.2. GRAPHING TRIGONOMETRIC FUNCTIONS 407
Lastly, we notice that this graph starts with a y-value of 0, then goes to the maximum,
back through 0 to the minimum and then back to zero to form one complete
wave. This is the signature of a sine function, so the answer to this problem
would be:
y =3sin2x
Example 4
Deterimine an equation that satisfies the given graph.
5
0 9π
16
9π
8
27π
16
9π
4
−5
First note that the maximum y-value for the graph is 5 and the minimum is −5.
This means that the amplitude is 5. Next we see that there is one complete period
of the function between 0 and 9π 4 , this means that the period is 9π 4
. From this
information, we know that A =5and that the period for the graph is 9π 4 . Since
P = 2π 2π
B
, and B =2π
P
, then B =
( 9π )=2π∗ 4
9π =8 9 .
4