College Algebra & Trigonometry, 2018a

430 CHAPTER 9. GRAPHING THE TRIGONOMETRIC FUNCTIONS
y-axis
Amplitude= |A|
Vertical Shift= D
x-axis
Period= 2π B
Phase Shift=− C B
y =4sin2(x+ π 3 ) − 1.
The amplitude in this problem is 4 and the vertical shift is −1.
The period for this graph is 2π B =2π 2
= π. Notice that the value of B is 2 in this
example, even though it’s been factored out from the rest of the argument.
The new starting point for the graph is actually easier to find in problems of this
type. If we take the argument as it is and set it equal to zero:
2(x+ π 3 )=0
we can divide through on both sides by 2 to cancel out the factor of B:
2(x+ π 3 )
2
= 0 2
x+ π 3 =0
x =− π 3
So, the new starting point for the function is − π 3 .
Now let’s find the rest of the critical values along the x-axis. The period for this
graph is π, so the “jump” between the critical values along the x-axis will be:
π∗ 1 4 =π 4