1. 11-3 polar functions

2. take “times” to smell the roses
There are three major types of graphs you should know how to graph by hand on the AP Calculus BC Exam:
petal graphs, limaçons, and lemniscates.
PETAL GRAPHS/ROSES
take “times” to smell the roses
Petal graphs are in the form
Radius (length of petal): a
(Note, it’s always 2n, but in the odd cases, the second set overlaps the first set.)
First Peak for Cosine:
First Peak for Sine:
(offset)
Number of Petals if n is odd: n
odd man out
pi for 2 people
Number of Petals if n is even: 2n
How far apart?
even Steven

3. Ex 1)
Maximum Radius:
Number of Petals:
First Peak at:
Each petal is radians apart. 6 3

4. Ex 2)
Maximum Radius:
Number of Petals:
First Peak at:
Each petal is radians apart. 5 4

5. These are equations of the form snails
LIMAÇONS
These are equations of the form
snails
Orientation: Cosine: on x-axis Sine: on y-axis
+: right –: left +: up –: down
Lengths to place points:
Larger Side: a + b Smaller Side: a – b Bumps: a
Shapes:
Cardioid Looped Limaçon
Small person can loop over
Healthy Steady Heartbeat

6. Slightly bigger friend dents hood of car with
Shapes:
Dented Limaçon
Slightly bigger friend dents hood of car
with
a “slightly” larger than b
Convex Limaçon
with
a “WAY” larger than b
Way bigger friend gets a flat bench
(at least twice as big)

7. Ex 3)
Oriented: on x-axis right
Shape: Looped
Ex 4)
Oriented: on y-axis down
Shape: Cardioid

8. Ex 5)
Oriented: on x-axis left
Shape: Dented
Ex 6)
Oriented: on y-axis up
Shape: Convex (flat)

9. LEMNISCATES
Lemniscates are in the form
in a figure 8 on a double date
Cosine lemniscates are always oriented: on x-axis
Sine lemniscates are always oriented:
Maximum distance out is:

10. Ex 7)
Oriented:
Maximum Distance Away from Pole:

11. CIRCLES
Circles are in the form
Orientation: Cosine: on x-axis Sine: on y-axis
+: right –: left +: up –: down
2. Diameter is: a

12. Ex 8)
Oriented: on x-axis left
Ex 9)
Oriented: on y-axis up