Pre-Calculus Lesson Plans Unit 8
Polar: May 11th to May 18th 2011
End of Year May 19th – June 2nd 2011
Date
Wednesday
May 11
Thursday
May 12
Friday
May 13
Monday
May 16
Objective
TSW be able to Convert between Polar &
Rectangular systems
Plot points on polar grid.
TSW do a Polar Graphing Discovery
Activity. Graph polar equations.
TSW be able to graph polar equations.
TSW be able to identify types of
graphs from equations.
Topic
Converting between Polar
and Rectangular systems.
Assignment
Worksheet
Discovery activity, graphing
polar equations.
Graphing polar equations
Quiz Converting
Identifying graphs from
Equations.
Worksheet
Worksheet
Worksheet
Tuesday
May 17
TSW come to class prepared with
review questions for test.
Review for Test
Study for
Test #8
Wednesday
May 18
Thursday
May 19
Friday
May 20
Monday
May 23
TSW demonstrate mastery of objectives
in this unit.
TSW graph polar equations for their
polar project. or EOC
TSW graph polar equations for their
polar project. or EOC
TSW graph polar equations for their
polar project. Review for exam.
Test #8
project
Work on polar project.
Review for exam
Project/ review
Tuesday
May 24
Wednesday
May 25
Thursday
May 26
Friday
May 27
Tuesday
May 31
Wednesday
June 1
Thursday
June 2
TSW take optional nine week test or
work on review .
TSW work on exam review.
Optional nine week test
Review for exam
Review for exam
review
TSW work on exam review.
Review for exam
Review/ study
6th period exams, no 7th period
Review /exam
Study
2nd and 4th exam, 5th and 7th period class
Review /exam
Study
3rd and 5th exam
Half day
Study
1st and 7th exam.
Half day
Have a great
Summer !!!
EOC / Work on polar project project
EOC / Work on polar project project
review
Grade
Polar Coordinates Notes
Name: __________________________
The Polar Coordinate System is an alternative to the Cartesian system of rectangular coordinates for locating
points in a plane. It consists of a fixed point O, called the pole or origin and a fixed ray OA, called the
polar axis with O as its initial point.
The polar coordinates of a fixed point P in the polar coordinate system consist of an ordered pair (r, θ).
The directed distance from the pole to P is R, and the measure of the angle from the polar axis to OP is θ.
P (r, θ)
O
A
Both r and θ can be either positive or negative.
When r is positive, the polar distance is measured from O along the terminal side of the angle θ, and
when r is negative, it is measured from O on the opposite the terminal side of θ.
When θ is positive, the polar angle is obtained by rotating OP counterclockwise from the polar axis,
and when θ is negative, the rotation is clockwise.
rθ- plane is a plane where polar coordinates (r, θ) are used to identify its points.
Examples. Graph:
1) P ( 5, 60° )
2) Q ( 5, -60° )
3) W ( -5, 60° )
4) V ( -5, -60° )
5) A ( 3 150º)
6) B (-3, -150º)
Rotations of θ and θ + 2nπ or θ + 360°n produce the same angle so there are infinitely many ways to
represent the same angle.
Examples:
1) Plot the point P (2, 45°) and find 3 other polar representations of the point.
2) Plot the point P (1, π) and find 3 other polar representations of the point.
Polar Equation: an equation with polar coordinates
Polar Graph: a graph of the set of all points (r, θ) that satisfy a given polar equation.
The two most basic polar equations are:
r = c a circle of radius c
r = θ a line through the origin that forms an angle θ with the polar axis
Examples.
1) Sketch r = 3.
2) Sketch r = –2.
3) Sketch r = 30°.
4) Sketch r = – 45°.
If you superimpose a Rectangular Coordinate system over a Polar Coordinate system:
y
r 2  x 2  y 2 so r =
x2  y2
P(x, y)
r
x
cos  
x
r
so x  r cos
sin  
y
r
so y  r sin 
tan  
y
x
polar axis
Convert from Rectangular to Polar Coordinates.
1) ( 3, 3)
2) (2, 2 3 )
3) (0, -2)
4) ( – 4 3 , 4)
3) ( -5, 240°)
4) (4,
Convert from Polar to Rectangular Coordinates.
1) (-2, π)
2) (3, 135°)

)
6
Convert the Polar Equations to Rectangular form
1) r = 1
2) θ = 45°
5) r  3sin 
6) r 
3) r  5 sec
6
2 cos   3 sin 
4) r  4 csc
7) r 
2
2  cos 
Convert the rectangular Equations to Polar form.
1) 5 x  7 y  12
2) x = 11
4) x 2  y 2  9
5) (y – 2)2 + x2 = 16
3) y = 6
Polar Coordinates Homework
Name: __________________________
Convert from Rectangular to Polar Coordinates then graph
A ( –3, 3 3 )
B (4, – 4 3 )
C (0, – 5)
D (– 3,1)
E (5, – 5)
Graph then, Convert from Polar to Rectangular Coordinates.
F (1,

)
2
G (6, 120°)
H ( 4, –270°)
Give 3 additional coordinates for the points given.
1)
( 1, 45º)
2) ( 2, 210°)
I (2,

)
4
J (3, π)
Convert the Polar Equations to Rectangular form
1) r = 3
2) θ = 30°
5) r  2 sin 
6) r 
4) r  8 csc
3) r  7 sec
5
4 cos   2 sin 
7) r 
3
1  sin 
Convert the rectangular Equations to Polar form.
1) 3x  5 y  8
2) x = 4
4) x 2  y 2  16
5) y2 + (x – 3)2 = 25
3) y = 9