7.1: Polar Necessities
This activity is intended to supplement Trigonometry, Chapter 6, Lesson 4.
ID: 12558
Time Required: 15 minutes
Activity Overview
Students will explore what is necessary to understand the calculus of polar equations. Students will graphically and algebraically find the slope of the tangent line at a point on a polar graph. Finding the area of a region of a polar curve will be determined using the area formula.
Topic: Polar Equations
 Find the slope of a polar equation at a particular point.
 Find the area of polar equation.
Teacher Preparation and Notes
 Make sure each students' calculator is in RADIANS (RAD) and POLAR (POL) in the MODE menu.
Associated Materials
 Student Worksheet: Trigonometric Patterns http://www.ck12.org/flexr/chapter/9704, scroll down to the third activity.
Plotting Coordinates & Exploring Polar Graphs
Students begin the activity by plotting points on a polar graph. This should be a refresher of polar coordinates for most students. Students practice using the calculator to graph a polar equation.
Discussion Questions

What do you think it means to have a negative angle, like
(−π3,3) ? 
What about if r was negative? For example, move to
(π2,−6) .
Solutions
1. See image below.
2. If
3. a heart or cardioid
4. A circle is in the form
A polar rose with even petals is in the form
A polar rose with odd petals is in the form
A limaçon with an inner loop comes form