Section 6.7 Polar Coordinates 113

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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). Larson/Hostetler Trigonometry, Sixth Edition Student Success Organizer IAE Copyright © Houghton Mifflin Company. All rights reserved. 114 Chapter 6 Topics in Analytic Geometry 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 Page(s) Exercises Larson/Hostetler Trigonometry, Sixth Edition Student Success Organizer IAE Copyright © Houghton Mifflin Company. All rights reserved. .

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