Answer:
Y
=
3
cos
(
2
x
-
1
)
Use the form
to
cos
(
b
x
-
c
)
+
d
to find the variables used to find the amplitude, period, phase shift, and vertical shift.
to
=
3
b
=
2
c
=
1
d
=
0
Find the amplitude
|
to
|
.
Amplitude:
3
Find the period using the formula
2
π
|
b
|
.
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Period:
π
Find the phase shift using the formula
c
b
.
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Phase shift:
1
2
Find the vertical displacement
d
.
Vertical displacement:
0
List the properties of trigonometric functions.
Amplitude:
3
Period:
π
Phase shift:
1
2
(
1
2
on the right)
Vertical displacement:
0
Select some points on the graph.
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x
F
(
x
)
1
2
3
π
4
+
1
2
0
π
2
+
1
2
-
3
3
π
4
+
1
2
0
π
+
1
2
3
The trigonometric function can be drawn using the amplitude, period, phase shift, vertical shift, and the points.
Amplitude:
3
Period:
π
Phase shift:
1
2
(
1
2
on the right)
Vertical displacement:
0
x
F
(
x
)
1
2
3
π
4
+
1
2
0
π
2
+
1
2
-
3
3
π
4
+
1
2
0
π
+
1
2
3Y
=
3
cos
(
2
x
-
1
)
Use the form
to
cos
(
b
x
-
c
)
+
d
to find the variables used to find the amplitude, period, phase shift, and vertical shift.
to
=
3
b
=
2
c
=
1
d
=
0
Find the amplitude
|
to
|
.
Amplitude:
3
Find the period using the formula
2
π
|
b
|
.
Tap for more steps ...
Period:
π
Find the phase shift using the formula
c
b
.
Tap for more steps ...
Phase shift:
1
2
Find the vertical displacement
d
.
Vertical displacement:
0
List the properties of trigonometric functions.
Amplitude:
3
Period:
π
Phase shift:
1
2
(
1
2
on the right)
Vertical displacement:
0
Select some points on the graph.
Tap for more steps ...
x
F
(
x
)
1
2
3
π
4
+
1
2
0
π
2
+
1
2
-
3
3
π
4
+
1
2
0
π
+
1
2
3
The trigonometric function can be drawn using the amplitude, period, phase shift, vertical shift, and the points.
Amplitude:
3
Period:
π
Phase shift:
1
2
(
1
2
on the right)
Vertical displacement:
0
x
F
(
x
)
1
2
3
π
4
+
1
2
0
π
2
+
1
+
1
2
0
π
+
1
2
3