College Algebra & Trigonometry, 2018a

406 CHAPTER 9. GRAPHING THE TRIGONOMETRIC FUNCTIONS
Determining an equation from a graph
Sometimes, you will be given a graph and asked to determine an equation which
satisfies the conditions visible in the graph. So far, we have only discussed two of
the possible transformations of a trigonometric function - the amplitude and period.
Remember that in an equation of the form y = A sin Bx or y = A cos Bx, the
amplitude is |A| and the period is 2π B
. So, to write an equation for a trigonometric
function, we need to determine the values of A and B.
Example 3
Deterimine an equation that satisfies the given graph.
3
2
1
−1
0
π
4
π
2
3π
4
π
−2
−3
First note that the maximum y-value for the graph is 3 and the minimum is −3.
This means that the amplitude is 3. Next we see that there is one complete period
of the function between 0 and π, this means that the period is π. From this
information, we know that A =3and that the period for the graph is π. Since the
period P = 2π B
, then we know that B =2π
P . So, B =2π π =2.