Lectire 33: Sketching and Area of Polar
Curves
Areas in Polar Coordinates
Formula for the area of a sector of a circle
A
=
1
2
r
2
where
r
is the radius and
is the radian measure
of the central angle.
Area of the polar region bounded by a polar
curve
r
=
f
( ) and by the rays
=
and
=
is
A
=
R
1
2
r
2
d
1

ex.
Graph the polar curve and
nd the area
enclosed by the curve:
(
2
)
r
= cos 2
2

ex.
Graph the curve and
nd the area enclosed:
r
= 2(1
sin
)
(6 )
3

ex.
Graph the curve and
nd the area of the
inner loop:
r
= 1
3 cos
:
(
11
2
arccos
1
3
3
p
2)
4

ex.
Graph the curves and
nd the area inside
the
rst curve