April 22, 2015
(6.4) Polar Coordinates
Objective: To learn about the Polar Coordinate System, and convert points and equations between rectangular and polar systems.
Why: The use of polar coordinates sometimes simplifies complicated rectangular equations and they are useful in calculus.
April 22, 2015
(r, O)
Obj: To learn about the Polar Coordinate System, and convert points and equations between rectangular and polar systems.Polar Coordinate System
April 22, 2015
Plotting Points.
1. A(2, 3)
Obj: To learn about the Polar Coordinate System, and convert points and equations between rectangular and polar systems.
2. B(-3, )π
4
3. C(-4, - )7π
6
April 22, 2015
Complete Worksheet Side 1.
April 22, 2015
Convert the polar coordinates to rectangular coordinates.
1. (2, )
Obj: To learn about the Polar Coordinate System, and convert points and equations between rectangular and polar systems.
April 22, 2015
2. (3 , 3)
Obj: To learn about the Polar Coordinate System, and convert points and equations between rectangular and polar systems.
April 22, 2015
Convert the rectangular coordinates to polar coordinates.
1. ( -1, 1)
Obj: To learn about the Polar Coordinate System, and convert points and equations between rectangular and polar systems.
April 22, 2015
2. (1, -2)Obj: To learn about the Polar Coordinate System, and convert points and equations between rectangular and polar systems.
April 22, 2015
Obj: To learn about the Polar Coordinate System, and convert points and equations between rectangular and polar systems.
HW:
(Reg): (6.4) Pg.492: 1-4, 7-15, 19-21, (27 and 29 give rectangular coordinates only)
April 22, 2015
Plot the point (3, ). Then give 3 additional representations for the point. Then convert the point to rectangular coordinates.
π
6
April 22, 2015
Obj: To learn about the Polar Coordinate System, and convert points and equations between rectangular and polar systems.
Coordinate Conversion
x = r cos O
y = r sin O
r
x
y
O
tan O =
r2 = x2 + y2
yx
April 22, 2015
Describe the graph of each polar equation and find the corresponding rectangular equation.
1. r = 3
Obj: To learn about the Polar Coordinate System, and convert points and equations between rectangular and polar systems.
April 22, 2015
2. O = 3
Obj: To learn about the Polar Coordinate System, and convert points and equations between rectangular and polar systems.
April 22, 2015
3. r = sec O
Obj: To learn about the Polar Coordinate System, and convert points and equations between rectangular and polar systems.
April 22, 2015
Obj: To learn about the Polar Coordinate System, and convert points and equations between rectangular and polar systems.
4. r = -3sinθ
April 22, 2015
Obj: To learn about the Polar Coordinate System, and convert points and equations between rectangular and polar systems.
Convert the rectangular equation to a polar equation.
5. x = 2 6. x2 + y2 = 16
7. (x-3)2 + y2 = 9 8. y = x2
April 22, 2015
Equation Conversion
1. Convert y = x2 to a polar equation.
Obj: To learn about the Polar Coordinate System, and convert points and equations between rectangular and polar systems.
r
(x,y)
x
yθ
April 22, 2015
Obj: To learn about the Polar Coordinate System, and convert points and equations between rectangular and polar systems.
HW:
(REG) (6.4) Pg.492: 35, 37, 39, 43, 47
