Pre-Calculus Honors

Book Reference 6.4

Unit 9 Lesson 8: Polar Coordinates

Objective: ______

Do Now: Read and mark up the following text

So far you have been representing graphs of equations as a collection of points (x, y) on the rectangular coordinate system, where x and y the directed the distances from the coordinate axes to the point (x, y). In this lesson you will study a second coordinate system called the polar coordinate system.

To form the polar coordinate system in the plane at a fix point O, called the pole or origin, and construct from O an initial ray called the polar axis. Then each point P in the plane can be assigned polar coordinates as follows.

1.  r = directed distance from O to P.

2.  = directed angle, counterclockwise from the polar axis to the segment

1. Guided Practice: Plotting Basic Polar Coordinate Points

Numerical / Graphical
A
B
C
D
E /

3.  Guided Practice: Converting Between Polar Coordinates and Rectangular Coordinates

Verbal / Diagram
When we use both polar coordinates and Cartesian coordinates, the pole is the origin and the polar axis is the positive x axis. By applying trigonometry, we can find equations that relate polar coordinates and the rectangular coordinates (x, y) or a point P. /
Algebraic / Numerical
Write a set of equations that represents the conversion of polar coordinates to rectangular coordinates.
X =
Y= / Find the rectangular coordinates of the points with the given polar coordinates without a calculator.
a.)
b.)
Verbal / Diagram
When we use both polar coordinates and Cartesian coordinates, the pole is the origin and the polar axis is the positive x axis. By applying trigonometry, we can find equations that relate polar coordinates and the rectangular coordinates (x, y) or a point P. /
Algebraic / Numerical
Write a set of equations that represents the conversion of rectangular coordinates to polar coordinates.
r =
/ Find the two polar coordinates for the point with the given rectangular coordinates.
a.)
Algebra / Diagram
b.)
Algebra / Diagram

Pre-Calculus Homework Pg 539 # (1, 5, 7, 9, 13, 12, 15, 17)