Answer:
Amplitude of
4
sin
(
3
x
)
is
4
Period of
4
sin
(
3
x
)
is
6
π
Explanation:
y
=
sin
(
θ
)
has an amplitude of
1
XXXX
y
varies between
+
1
and
−
1
If
y
=
4
sin
(
θ
)
XXXX
then
y
will vary between
+
4
and
−
4
XXXX
→
y
=
4
sin
(
θ
)
has an amplitude of
4
(for any
θ
)
y
=
k
⋅
sin
(
θ
)
has a period of
2
π
XXXX
y
completes one cycle while
θ
increases by
2
π
if
3
x
=
θ
XXXX
y
completes one cycle while
3
x
increases by
2
π
XXXX
or (expressed in another way)
XXXX
y
completes
1
3
of a cycle while
x
increase by
2
π
XXXX
⇒
y
completes 1 cycle while
x
increases by
3
×
2
π
=
6
π