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Mathematics
Mathematics
Problem
Let
A
1
A_1
A
1
be the area enclosed by
r
=
a
sin
θ
r=a\sin\theta
r
=
a
sin
θ
on
0
≤
θ
≤
π
0\le\theta\le\pi
0
≤
θ
≤
π
, and let
A
2
A_2
A
2
be the area enclosed by
r
=
a
sin
2
θ
r=a\sin 2\theta
r
=
a
sin
2
θ
on
0
≤
θ
≤
π
2
0\le\theta\le\tfrac{\pi}{2}
0
≤
θ
≤
2
π
, where
a
>
0
a>0
a
>
0
. What is the value of the ratio
A
1
A
2
\dfrac{A_1}{A_2}
A
2
A
1
? a)
1
1
1
b)
2
2
2
c)
1
2
\dfrac{1}{2}
2
1
d) 4
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