MATH109 HW 5: 10.3 - 10.4
DUE 3/14-16 IN RECITATION
Find a polar equation for the curve represented by the given Cartesian equation.
1.
y = 1 + 3x
2.
x2 − y2 = 4
Find a Cartesian equation for the curve.
3.
r = 4 sec θ
4.
r2 sin 2θ = 1
5-7. Find the area enclosed by the curve. From left to right:
5.
r = 2 + cos θ
6.
r = 1 − sin θ
7.
r = 2 + sin 4θ
y
y
y
x
x
x
8-10. Find the area of the region that lies inside the first curve and outside the second curve. In the
pictures below, you can easily tell which curve is the first and which is the other. From left to right:
8. r = 1 + cos θ;
9.
r = 1 − sin θ;
10. r = 3 sin θ;
r = 2 − cos θ
r=1
r = 2 − sin θ
1
2
MATH109 HW 5: 10.3 - 10.4 DUE 3/14-16 IN RECITATION
y
y
y
x
x
x
11-12. Find the area of the region that lies inside both curves.
11. r = 1 + cos θ;
12 . r = 2 + 2 cos θ;
∗
r = 1 − cos θ
r = 2 + sin θ
y
y
x
x