A lesson on construction is motivated by the need to construct the diagonal of a unit square.
A Lesson in Construction
Tuyetdong Phan-Yamada and Walter M. Yamada III
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