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Mathematics
Mathematics
Problem
Let
R
R
R
,
S
S
S
, and
T
T
T
be three polar curves on
0
≤
θ
≤
π
0\le \theta \le \pi
0
≤
θ
≤
π
defined respectively by
r
=
sin
θ
r=\sin\theta
r
=
sin
θ
,
r
=
1
2
+
sin
θ
r=\dfrac12+\sin\theta
r
=
2
1
+
sin
θ
, and
r
=
1
+
sin
θ
r=1+\sin\theta
r
=
1
+
sin
θ
. Rank the areas
A
R
A_R
A
R
,
A
S
A_S
A
S
, and
A
T
A_T
A
T
enclosed by the curves from least to greatest. a)
A
S
<
A
R
<
A
T
A_S < A_R < A_T
A
S
<
A
R
<
A
T
b)
A
R
<
A
S
<
A
T
A_R < A_S < A_T
A
R
<
A
S
<
A
T
c)
A
R
=
A
S
=
A
T
A_R = A_S = A_T
A
R
=
A
S
=
A
T
d)
A
R
<
A
T
<
A
S
A_R < A_T < A_S
A
R
<
A
T
<
A
S
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