First, students will learn how to convert points between polar and Cartesian form. Then students will learn how to convert equations between polar and Cartesian form.
Converting between polar and Cartesian form
Concude by giving your students this challenge:
Find \(x{:}\)
There are two elegant ways to solve this problem, both of which can be done mentally. Here's the first way: Notice that \(ACEDB\) is a pentagon, and thus, it's interior angles sum to \(540^\circ.\) Notice that \(\angle DEC = 360^\circ - 160^\circ = 200^\circ.\) Adding up the known angles in the pentagon, gives us \(80^\circ + 20^\circ + 200^\circ + 10^\circ = 310^\circ.\) But we need \(540^\circ,\) so the missing angle, \(\angle BDE,\) must be \(230^\circ.\) Thus, \(x = 360^\circ - 230^\circ = 130^\circ.\) Here's the second way: Start by drawing \(\overline{BC}.\) Notice that \(\triangle ABC\) has \(80^\circ + 20^\circ + 10^\circ = 110^\circ,\) so it's lacking \(70^\circ.\) Also, notice that \(BDEC\) is a quadrilateral, and thus, it's interior angles sum to \(360^\circ.\) Adding up the known angles in the quadrilateral, gives us \(160^\circ + 70^\circ = 230^\circ,\) but we need \(360^\circ,\) so \(x = 360^\circ - 230^\circ = 130^\circ.\)