1. 10.2 Graphing Polar Equations Day 1

2.  SPIRAL
Also called the “Spiral of Archimedes”
No special rules!
Typical Graph:

3. If we did a table, this is what it would look like 6 5.2
EX 1: θ r
If we did a table, this is what it would look like 6
5.2
This is a polar grid.
Famous angles are illustrated.
Concentric circles represent the values of r.
4.2 3 –3
–4.2
–5.2 –6
–5.2
–4.2 –3
these points are on top of other points! 3
4.2
5.2 6

4. CIRCLES There are three forms for a circle.
Center of circle at _______
Radius = _______
Typical Graph:
Contains the _______
Tangent to _______
Center on _______
Diameter = _______
If a > 0, circle is ____ of pole
If a < 0, circle is ____ of pole
 Typical Graph:
pole
pole
pole k
polar axis
polar axis N E S W

5. EX 2:
Radius:______
Center On: Polar Axis /
Circle is N S E W of the pole 4

6. EX 3: θ r 2 3
3.4
3.7 4 1
0.6
0.3

7. LIMAÇONS French for “snail.” OR
(oriented on polar axis) (oriented on )
Limaçon with Inner Loop
When or a < b
Diameter = _______
Inner Loop = _______
Cardioid (heart-shaped)
When or a = b
Diameter
= _______ = ______
Dimpled Limaçon
When
Larger = _______
Smaller = _______
Convex Limaçon
When or a ≥ 2b
For all the “bumps,” they hit the polar axis or (whichever is the opposite of where it is oriented) at _______
Typical Graph: ±a a a 2a
larger a a a
diam
smaller
larger
inner
loop a
smaller a a

8. Limaçon with Inner Loop Cardioid Convex Limaçon
Type:__________________
On: Polar Axis /
Lengths:_________________
_________________________
EX 5:
On: Polar Axis /
EX 6:
(WEST)
Limaçon with Inner Loop
(same as r = 2 + 2sin )
Cardioid
Convex Limaçon
Oriented
Oriented
Oriented
Diam: 6
Diam: 4
Larger: 6
Inner Loop: 2
Smaller: 2

9. Ex 7: Determine an equation of the polar graph.
r = 5 + 3sin θ
Equation:_________________________________________________
Why?____________________________________________________
_________________________________________________________
Dimpled Limaçon on
 sin
North of pole  (+)
larger = 8
smaller = 2
bump hits at 5  a = 5
& since a + b = 8 & a – b = 2
 b = 3