r=2cos6(theta)?

Question

theta varies from 0 to 2pi. How many petals are generated?

Answer 1

first divide [0,2pi] into 6 intervals [0,2pi/6],[2pi/6,4pi/6],[4pi/6,6pi/6] amd so on

Now let's look to [0,2pi/6]. Since cos is periodic the graph on other intervals will be the same as on [0,2pi/6]
Even on [0,2pi/6] we have to restrict more and exclude the case when cos(6 theta) is negative since R is always non-negative.
Now if we take R=2cos(theta) you will obtain a circle, since it's R=2cos6(theta) this circle would be compressed, you obtain a "petal"
Now since this repeats 6 times you get 6 "petals"( but on the graph you see only one)

Answer 2

12

When coeffecient to the theta is even, you get 2 times the coeffecient number of petals.

Answer 3

b-smaga + balabooga times sega, DUH!! u dont knoe that!?