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7.1: Polar Necessities

Difficulty Level: At Grade Created by: CK-12
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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

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).


1. See image below.

2. If r(θ)=cos(θ),r(π3)=0.5.

3. a heart or cardioid

4. A circle is in the form r=a, where a is a constant.

A polar rose with even petals is in the form r(θ)=asin(nθ), where n is even.

A polar rose with odd petals is in the form r(θ)=asin(nθ), where n is odd.

A limaçon with an inner loop comes form r(θ)=b+acos(θ), where b<a.

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Date Created:
Feb 23, 2012
Last Modified:
Nov 04, 2014
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