The graph is commonly known as a rose.
k determines the number of petals. If k is
ODD: k petals
k is congruent to 1 mod 4: the axis petal is on the positive y-axis.
k is congruent to 3 mod 4: the axis petal is on the negative y-axis.
EVEN: 2k petals
a determines the radius of the rose. The radius of the rose is 2a.
If either, a or k is negative, the graph is reflected about the x-axis. If BOTH a and k are negative, then the graph is the same as if both were positive.
r = 2(3) sin (5q): A rose with 5 petals and a radius of 6. The axis petal is on the positive y-axis.
r = 2(-3) sin (5q): A rose with 5 petals and a radius of 6. The axis petal is on the negative y-axis.
r = 2(3) sin (-5q): A rose with 5 petals and a radius of 6. The axis petal is on the negative y-axis.
r = 2(5) sin (15q): A rose with 15 petals and a radius of 10. The axis petal is on the negative y-axis.
r = 2(-5) sin (15q): A rose with 15 petals and a radius of 10. The axis petal is on the positive y-axis.
r = 2(5) sin (-15q): A rose with 5 petals and a radius of 6. The axis petal is on the positive y-axis.
r = 2(7) sin (4q): A rose with 8 petals and a radius of 14.
r = 2(-7) sin (6q): A rose with 12 petals and a radius of 14.