Polar Graphing Investigation

Polar Graphing Investigation Explore the families of polar functions listed below. In each case, graph several examples by selecting different values for the parameters (control numbers) used in the equation. Describe the graphical features for that family. a) θ = k b) r = k c) r = k∙sin θ d) r = k∙cos θ e) r = f) r = g) r = a∙sin θ + b h) r = a∙cos θ + b i) r = a∙sin (b∙θ) j) r = a∙cos (b∙θ) Here are some guidelines for the presentation of your investigation: Graph each family of functions on a separate polar plane. On every graph, label each function and the polar plane. Describe the graphical features of each family: o What is common to all members of the family? o What is different about each member within the same family? Your final product will be either a poster presentation (see Mr. Stagg for posterboard) or an electronic presentation (i.e. Powerpoint).

A Rubric is on the back side of this sheet.

Rubric – Polar Graphing Investigation The following rubric describes the scaffolded levels of achievement for this project. A 3 is considered to show competency, while a 1 or a 2 indicate progress toward that level. A 4 indicates mastery of the skill.

4

Graph all 10 functions, each family on a separate graph Label each family member and all parts of the polar plane Describe the graphical features of each family: What is common to all members? What is different?

3

Graph the first 6 functions, each family on a separate graph Label each family member and all parts of the polar plane Describe the graphical features of each family: What is common to all members? What is different?

2

Graph 4 or 5 of the functions More than one family per graph Missing labels Descriptions of graphical features are incomplete

1

Fewer than 4 graphs No labels Missing descriptions