Section 6.7 Polar Coordinates 113

Course Number Section 6.7 Polar Coordinates Instructor Objective: In this lesson you learned how to plot points in the polar coordinate system and write equations in polar form. Date

I. Introduction (Pages 476-477) What you should learn How to plot points in the To form the polar coordinate system in the plane, fix a point O, polar coordinate system 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) q = directed angle, counterclockwise from polar axis to the segment from O to P

In the polar coordinate system, points do not have a unique representation. For instance, the point (r, q) can be represented as (r, q ± 2np) or (- r, q ± (2n + 1)p) , where n is any integer. Moreover, the pole is represented by (0, q), where q is any angle .

Example 1: Plot the point (r, q) = (- 2, 11p/4) on the polar py/2 coordinate system.

p x0

3p/2

Example 2: Find another polar representation of the point (4, p/6).

Answers will vary. One such point is (- 4, 7p/6).

II. Coordinate Conversion (Pages 477-478) What you should learn How to convert points The polar coordinates (r, q) are related to the rectangular from rectangular to polar coordinates (x, y) as follows . . . form and vice versa

x = r cos q y = r sin q

tan q = y/x r2 = x2 + y2

Example 3: Convert the polar coordinates (3, 3p/2) to rectangular coordinates. (0, - 3)

III. Equation Conversion (Page 479) What you should learn How to convert equations To convert a rectangular equation to polar form, . . . from rectangular to polar simply replace x by r cos q and y by r sin q, and simplify. form and vice versa

Example 4: Find the rectangular equation corresponding to the - 5 polar equation r = . sinq y = - 5

py/2 py/2 py/2

p x0 p x0 p x0

3p/2 3p/2 3p/2 Homework Assignment

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