Common Polar Curves (continued)
p. 555 - 556 (10.3)
Roses
r = a sin nθ  , n odd
0≤θ≤π
n petals
y-axis symmetry
r = 4 sin(3theta)
4
3
2
1
-4 -3 -2 -1
-1
-2
-3
-4
# 38b
r = a sin nθ  , n even
0 ≤ θ ≤ 2π
2n petals
x-axis and y-axis symmetry
r = 2 sin(4theta)
3
2
1
1 2 3 4
-3 -2 -1
1
2
3
-1
-2
-3
r = a cosnθ  , n odd
0≤θ≤π
n petals
x-axis symmetry
r = a cosnθ  , n even
0 ≤ θ ≤ 2π
2n petals
x-axis and y-axis symmetry
r = 4 cos(3theta)
4
3
2
1
r = 2 cos(4theta)
3
-4 -3 -2 -1
-1
-2
-3
-4
-3 -2 -1
1 2 3 4
2
1
1
-1
-2
-3
2
3