09.2­9.3 Polar Graphs and Equations.notebook
January 30, 2014
Unit 9, Polar Coordinates
9.2 Polar Graphs
9.3 Polar Form of a Linear Equation
NCSCOS 2.05, "Use polar coordinates to model and
solve problems."
WIMD: What I must do:
• I will graph a polar equation using the graphing calculator.
• I will graph a system of polar equations and determine a solution if one exists.
• I will convert between polar and rectangular coordinates.
Key words:
pole
polar coordinate system
polar ray
I will graph a polar equation using the graphing calculator.
Set calculator mode to: "POL" and "SIMUL."
Graph some of the following:
Function
xmin
xmax ymin
ymax
r=sinθ
-1.5
1.5
-1
1
r=cosθ
-1.5
1.5
-1
1
r=3-5cosθ -8
8
-6
6
r=3sin2θ -4.5
4.5
-3
3
6
-4
4
15
-10
10
r=2.5+2.5cosθ -6
r=.005θ
-15
0<θ<3600
1
09.2­9.3 Polar Graphs and Equations.notebook
January 30, 2014
I will graph a system of polar equations and determine a solution if one exists.
Caution: The intersection of a system of equations is
not always a solution. solve algebraically also...
Graph: r=3-3sinθ, r=4-sinθ
θ=210o
x=-3.89
y=-2.25
r= 4.5
θ=330o
x=3.89
y=-2.25
r= 4.5
Solve algebraically...
Graph: r=sinθ, r=1
Common Point:
r=1
θ=90o
Solve algebraically...
2
09.2­9.3 Polar Graphs and Equations.notebook
January 30, 2014
I will convert between polar and rectangular coordinates.
x = r*cosθ
y = r*sinθ
r
y
θ
x
Find the rectangular coordinates for each polar point.
D(-2, -5π /6)
C(3, 270o)
3
09.2­9.3 Polar Graphs and Equations.notebook
January 30, 2014
• I will convert between rectangular and polar coordinates.
r
y
θ
x
Convert to polar coordinates using radians for theta:
(2, -4)
(4.47, -1.11)
(-8, 12)
(14.42, 2.16)
4
09.2­9.3 Polar Graphs and Equations.notebook
January 30, 2014
Write the polar equation in rectangular form:
x2 + y2 = 6x
r = 6cosθ
Hint: Multiply both sides by r.
Write the rectangular equation in polar form:
r = 6cosθ
(x ­ 3)2 + y2 = 9
5
09.2­9.3 Polar Graphs and Equations.notebook
January 30, 2014
Write the polar equation in rectangular form:
x2 + y2 = 6x
r = 6cosθ
Express answer in (x-a)2 + (y-b)2 = r2
Hint: solve using completing the square."
Access Code: E7BE47BB9B
Glencoe Quizzes
Homework Assignment for 9.2­9.3
p565 #25­30
p571 14­39 odd
6
09.2­9.3 Polar Graphs and Equations.notebook
January 30, 2014
p565 #25­30
7
09.2­9.3 Polar Graphs and Equations.notebook
January 30, 2014
p571 14­39 odd
8
Attachments
Glencoe Pre­Calc on line quizzes