Pre-Calc Unit 14: Polar Assignment Sheet April 27 th to May 7 th 2015 Page 1 Date Objective/ Topic Assignment Did it Monday April 27 th Polar Discovery Activity pp. 4 - 5 Tuesday April 28 th Converting between Polar and Rectangular systems. Notes pp. 6 - 8 pp. 9 - 10 Wednesday April 29 th Graphing Polar Equations Notes p. 11 pp. 12 - 13 Thursday April 30 th Writing Equations from Graphs Notes p. 14 p. 15 review p.16 Friday May 1 st Unit 14 Review pp. 17 -18 study Monday May 4 th Unit 14 test Tuesday May 5 th Work on Polar Project Work on project Wednesday May 6 th Work on Polar Project Work on project Thursday May 7 th Work on then Turn in Polar Project Print out last unit
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Pre-Calc Unit 14: Polar Assignment Sheet
April 27th to May 7
th 2015
Page 1
Date Objective/ Topic Assignment Did it
Monday
April 27th
Polar Discovery Activity pp. 4 - 5
Tuesday
April 28th
Converting between Polar and
Rectangular systems.
Notes pp. 6 - 8
pp. 9 - 10
Wednesday
April 29th
Graphing Polar Equations
Notes p. 11
pp. 12 - 13
Thursday
April 30th
Writing Equations from Graphs
Notes p. 14
p. 15 review
p.16
Friday
May 1st
Unit 14 Review pp. 17 -18 study
Monday
May 4th
Unit 14 test
Tuesday
May 5th
Work on Polar Project Work on project
Wednesday
May 6th
Work on Polar Project Work on project
Thursday
May 7th
Work on then Turn in Polar Project
Print out last unit
POLAR GRAPHS DISCOVERY ACTIVITY
Put your graphing calculator in POLAR mode and RADIAN mode. Graph the following equation on your calculator,
sketch the graphs on this sheet, and answer the questions.
1. r 2cos 2. r 3cos 3. r 3cos
4. r 2sin 5. r 3sin 6. r 3sin
7. What is similar about the graphs of #1-3? 8. How are they different?
9. What is similar about the graphs of #4-6? 10. How are they different?
Page 2
11. r 2 2cos 12. r 1 2cos 13. r 2 cos
14. r 2 2sin 15. r 1 2sin 16. r 2 sin
17. What is similar about the graphs of #11-13? 18. How are they different?
19. What is similar about the graphs of #14-16? 20. How are they different?
Page 3
Put your graphing calculator in POLAR mode and RADIAN mode. Graph the following equation on your calculator,
sketch the graphs on this sheet, and answer the questions.
1. r 2cos3 2. r 3cos5 3. r 4cos7
4. r 2sin3 5. r 3sin5 6. r 4sin7
7. How does the coefficient affect the graphs?
8. How does the coefficient of the affect the graphs?
Page 4
9. r 3cos2 10. r 2cos 4 11. r 4cos6
12. r 3sin2 13. r 2sin4 14. r 4sin6
15. How does the coefficient affect the graphs?
16. How does the coefficient of the affect the graphs?
Page 5
Polar Coordinates Notes
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 2) Plot the point P (1, π) and find 3 other
polar representations of the point. polar representations of the point.
Page 6
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
θ = a line through the origin that forms an angle θ with the polar axis