Answer:
The graph belongs to the conic family called circle. Assign several values for
θ
then compute corresponding
r
then plot the graph
Explanation:
The given
r
=
4
sin
θ
is equivalent to
x
2
+
y
2
=
4
y
and by completing the square
x
2
+
y
2
−
4
y
+
4
−
4
=
0
(
x
−
0
)
2
+
(
y
−
2
)
2
=
4
also using the "center-radius form#
(
x
−
h
)
2
+
(
y
−
k
)
2
=
r
2
(
x
−
0
)
2
+
(
y
−
2
)
2
=
2
2
center
(
h
,
k
)
=
(
0
,
2
)
with radius
r
=
2
now, you are ready to graph
kindly see the graph below
graph{x^2+y^2=4y[-10,10,-5,5]}
You may also use
r
=
4
sin
θ
right away by assigning values for
θ
and noting all
(
r
,
θ
)
coordinates.
Step-by-step explanation:
