Lesson 15 polar curves
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This document provides an overview of polar curves and coordinates. It defines polar coordinates, explains how to plot points in a polar coordinate system, and how to convert between polar and rectangular coordinates. Examples are given to plot points with polar coordinates and express rectangular coordinates in terms of polar coordinates. Finally, common polar curves such as the cardiod, limacon, roses, spirals, and lemniscate are listed.
Lesson 15 polar curves
- 1. POLAR CURVES Prepared by: Prof. Teresita P. Liwanag – Zapanta B.S.C.E., M.S.C.M., M.Ed. (Math-units), PhD-TM (on-going)
- 2. SPECIFIC OBJECTIVES: At the end of the lesson, the student is expected to be able to: • define polar coordinates. • plot points polar coordinates. • write and sketch the graphs of polar equations. • convert polar to rectangular and vice versa.
- 5. Examples: Plot the given points on a polar coordinate system. b.P (3, 45°) b. P (3, –60°)
- 6. c. P (–3, 220°) d. P (-3, –75°)
- 7. RELATIONS BETWEEN RECTANGULAR AND POLAR COORDINATES The transformation formulas that express the relationship between rectangular coordinates and polar coordinates of a point are as follows: and Also, ; ;
- 9. 2. Express the rectangular coordinates (-4, 3) in terms of polar coordinates.
- 14. Cardiod Limacon
- 15. Eight – leaf Rose Three – leaf Rose
- 16. Spiral of Archimedes Logarithmic Spiral
- 17. Lemniscate