Area Bounded By Two Polar Curves
AP Calculus BC · Flashcards · Application
AP CALCULUS BC · FLASHCARDS
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QUESTION
Determine the area between
r
=
1
+
sin
(
θ
)
r = 1 + \sin(\theta)
r
=
1
+
sin
(
θ
)
and
r
=
1
r = 1
r
=
1
for
θ
=
0
\theta = 0
θ
=
0
to
θ
=
π
\theta = \pi
θ
=
π
.
QUESTION
For
r
=
2
+
cos
(
θ
)
r = 2 + \cos(\theta)
r
=
2
+
cos
(
θ
)
, what is the maximum value of
r
r
r
?
QUESTION
For
r
=
4
cos
(
θ
)
r = 4\cos(\theta)
r
=
4
cos
(
θ
)
and
r
=
4
sin
(
θ
)
r = 4\sin(\theta)
r
=
4
sin
(
θ
)
, find the intersection points.
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ANSWER
θ
=
π
4
,
5
π
4
\theta = \frac{\pi}{4}, \frac{5\pi}{4}
θ
=
4
π
,
4
5
π
. Found by solving
4
cos
(
θ
)
=
4
sin
(
θ
)
4\cos(\theta) = 4\sin(\theta)
4
cos
(
θ
)
=
4
sin
(
θ
)
, so
tan
(
θ
)
=
1
\tan(\theta) = 1
tan
(
θ
)
=
1
.
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