Use the form
a
sin
(
b
x
−
c
)
+
d
a
sin
(
b
x
-
c
)
+
d
to find the variables used to find the amplitude, period, phase shift, and vertical shift.
a
=
3
a
=
3
b
=
1
3
b
=
1
3
c
=
0
c
=
0
d
=
0
d
=
0
Find the amplitude
|
a
|
|
a
|
.
Amplitude:
3
3
Find the period using the formula
2
π
|
b
|
2
π
|
b
|
.
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Period:
6
π
6
π
Find the phase shift using the formula
c
b
c
b
.
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Phase Shift:
0
0
Find the vertical shift
d
d
.
Vertical Shift:
0
0
List the properties of the trigonometric function.
Amplitude:
3
3
Period:
6
π
6
π
Phase Shift:
0
0
(
0
0
to the right)
Vertical Shift:
0
0
Select a few points to graph.
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x
f
(
x
)
0
0
3
π
2
3
3
π
0
9
π
2
−
3
6
π
0
x f
(
x
)
0 0
3
π
2
3 3π 0
9
π
2
-3 6π 0
The trig function can be graphed using the amplitude, period, phase shift, vertical shift, and the points.
Amplitude:
3
3
Period:
6
π
6
π
Phase Shift:
0
0
(
0
0
to the right)
Vertical Shift:
0
0
x
f
(
x
)
0
0
3
π
2
3
3
π
0
9
π
2
−
3
6
π
0
x f
(
x
)
0 0
3
π
2
3 3π 0
9
π
2
-3 6π 0
y
=
3
s
i
n
(
1
3
x
)
y
=
3
(
1
3
x
)