<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Dismiss
Skip Navigation

7.1: Polar Necessities

Difficulty Level: At Grade Created by: CK-12

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 ?
  • What about if r was negative? For example, move to .

Solutions

1. See image below.

2. If .

3. a heart or cardioid

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

A polar rose with even petals is in the form , where is even.

A polar rose with odd petals is in the form , where is odd.

A limaçon with an inner loop comes form , where .

Image Attributions

Show Hide Details
Files can only be attached to the latest version of section
Reviews
Help us create better content by rating and reviewing this modality.
Loading reviews...
Please wait...
Please wait...
Image Detail
Sizes: Medium | Original
 
TI.MAT.ENG.SE.1.Trigonometry.7.1

Original text