Exploroing Polar Curves with GeoGebra

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Most trigonometry textbooks teach the graphing of polar equations as a two-step process: (1) plot the points corresponding to values of θ such as π, π/2, π/3, π/4, π/6, and so on; and then (2) connect these points with a curve that follows the behavior of the trigonometric function in the Cartesian plane. Many students have difficulty using this method to graph general polar curves. The difficulty seems to stem from an inability to convert changes in the value of the trigonometric equation as a function of angle (abscissa vs. ordinate in Cartesian coordinates) to changes of the radius as a function of angle (r[θ] in polar coordinates). GeoGebra provides a tool to help students visualize this relationship, thus significantly improving students' ability

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Edited by Larry Ottmanlottman@gfsnet.org Germantown Friends School Philadelphia, PA

James Kettj.gkett@gmail.com Singapore-American High School (retired) Singapore

Contributor Notes

Tuyetdong Phanyamada, tphanyamada@yahoo.com, is a part-time instructor in the mathematics department at California State University of Los Angeles. She is interested in algebra, geometry, trigonometry, and calculus activities.

Walter M. Yamada III, walter.mas.yamada@gmail.com, is an associate professor of psychology at Azusa Pacific University and works with the Laboratory of Applied Pharmacokinetics at the University of Southern California in Los Angeles. He studies the mathematics of dynamic biological systems. The authors are husband and wife.

(Corresponding author is Phanyamada tphanyamada@yahoo.com)
(Corresponding author is Yamada walter.mas.yamada@gmail.com)
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