Period of 7 sin 8x is (2pi)/8 = pi/4
brief explain step by step
Answers
Answer:Since the period of sin(x) is 2π, the period of sin(
12
π[x]
), where [x] is a greatest integer function, is
12
π
2π
=24.
period of tanx is π and period of cosx is 2π
Similarly, the periods of cos(
4
π[x]
) and tan(
3
π[x]
) are 8 and 3 respectively.
Hence the period of the function sin(
12
π[x]
)+cos(
4
π[x]
)+tan(
3
π[x]
) is the LCM of the periods of the three functions added.
Hence the period of the given function is LCM (24,8,3)=24.
y
=
7
sin
(
π
8
x
)
Use the form
a
sin
(
b
x
−
c
)
+
d
to find the variables used to find the amplitude, period, phase shift, and vertical shift.
a
=
7
b
=
π
8
c
=
0
d
=
0
Find the amplitude
|
a
|
.
Amplitude:
7
Find the period using the formula
2
π
|
b
|
.
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Period:
16
Find the phase shift using the formula
c
b
.
Tap for more steps...
Phase Shift:
0
Find the vertical shift
d
.
Vertical Shift:
0
List the properties of the trigonometric function.
Amplitude:
7
Period:
16
Phase Shift:
0
(
0
to the right)
Vertical Shift:
0
Select a few points to graph.
Tap for more steps...
x
f
(
x
)
0
0
4
7
8
0
12
−
7
16
0
The trig function can be graphed using the amplitude, period, phase shift, vertical shift, and the points.
Amplitude:
7
Period:
16
Phase Shift:
0
(
0
to the right)
Vertical Shift:
0
x
f
(
x
)
0
0
4
7
8
0
12
−
7
16
0
y
=
7
sin
(
π
8
x
)
Use the form
a
sin
(
b
x
−
c
)
+
d
to find the variables used to find the amplitude, period, phase shift, and vertical shift.
a
=
7
b
=
π
8
c
=
0
d
=
0
Find the amplitude
|
a
|
.
Amplitude:
7
Find the period using the formula
2
π
|
b
|
.
Tap for more steps...
Period:
16
Find the phase shift using the formula
c
b
.
Tap for more steps...
Phase Shift:
0
Find the vertical shift
d
.
Vertical Shift:
0
List the properties of the trigonometric function.
Amplitude:
7
Period:
16
Phase Shift:
0
(
0
to the right)
Vertical Shift:
0
Select a few points to graph.
Tap for more steps...
x
f
(
x
)
0
0
4
7
8
0
12
−
7
16
0
The trig function can be graphed using the amplitude, period, phase shift, vertical shift, and the points.
Amplitude:
7
Period:
16
Phase Shift:
0
(
0
to the right)
Vertical Shift:
0
x
f
(
x
)
0
0
4
7
8
0
12
−
7
16
0
y
=
7
sin
(
π
8
x
)
Use the form
a
sin
(
b
x
−
c
)
+
d
to find the variables used to find the amplitude, period, phase shift, and vertical shift.
a
=
7
b
=
π
8
c
=
0
d
=
0
Find the amplitude
|
a
|
.
Amplitude:
7
Find the period using the formula
2
π
|
b
|
.
Tap for more steps...
Period:
16
Find the phase shift using the formula
c
b
.
Tap for more steps...
Phase Shift:
0
Find the vertical shift
d
.
Vertical Shift:
0
List the properties of the trigonometric function.
Amplitude:
7
Period:
16
Phase Shift:
0
(
0
to the right)
Vertical Shift:
0
Select a few points to graph.
Tap for more steps...
x
f
(
x
)
0
0
4
7
8
0
12
−
7
16
0
The trig function can be graphed using the amplitude, period, phase shift, vertical shift, and the points.
Amplitude:
7
Period:
16
Phase Shift:
0
(
0
to the right)
Vertical Shift:
0
x
f
(
x
)
0
0
4
7
8
0
12
−
7
16
0
y
=
7
sin
(
π
8
x
)
Use the form
a
sin
(
b
x
−
c
)
+
d
to find the variables used to find the amplitude, period, phase shift, and vertical shift.
a
=
7
b
=
π
8
c
=
0
d
=
0
Find the amplitude
|
a
|
.
Amplitude:
7
Find the period using the formula
2
π
|
b
|
.
Tap for more steps...
Period:
16
Find the phase shift using the formula
c
b
.
Tap for more steps...
Phase Shift:
0
Find the vertical shift
d
.
Vertical Shift:
0
List the properties of the trigonometric function.
Amplitude:
7
Period:
16
Phase Shift:
0
(
0
to the right)
Vertical Shift:
0
Select a few points to graph.
Tap for more steps...
x
f
(
x
)
0
0
4
7
8
0
12
−
7
16
0
The trig function can be graphed using the amplitude, period, phase shift, vertical shift, and the points.
Amplitude:
7
Period:
16
Phase Shift:
0
(
0
to the right)
Vertical Shift:
0
x
f
(
x
)
0
0
4
7
8
0
12
−
7
16
0
Step-by-step explanation: