College Algebra & Trigonometry, 2018a

414 CHAPTER 9. GRAPHING THE TRIGONOMETRIC FUNCTIONS
In this graph, the maximum y-value is 6 and the minimum y-value is −2. The
average of these two:
max+min
2
= 6+(−2)
2
= 4 2 =2=D
is the value of D, the vertical shift.
The distance between 6 and −2 is 6 − (−2) = 8. Half the distance between the
max and min is 4, which is the value of A.
max−min
2
= 6−(−2)
2
= 8 2 =4=A
The graph completes one full cycle between 0 and 3π, so the period would be 3π
and the value of B would be B = 2π
P =2π 3π =2 3
= B. So a correct equation for the
graph would be:
y =4sin 2 3 x +2