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Session 84: Polar Coordinates and Graphing

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Overview

Graphing curves described by equations in polar coordinates can be very rewarding, but we must be attentive when plotting points whose radii are negative. Occasionally it is helpful to convert from polar coordinates to Cartesian (xy) coordinates in order to better understand a curve.

Lecture Video and Notes

Video Excerpts

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» Clip 1: Graph of r = 2a cos(θ) (4 min)
» Accompanying Notes (PDF)

From Lecture 33 of 18.01 Single Variable Calculus, Fall 2006


» Clip 2: Graph of r = sin(2θ) (13 min)
» Accompanying Notes (PDF)

From Lecture 33 of 18.01 Single Variable Calculus, Fall 2006


» Clip 3: Polar Coordinates and Conic Sections (2 min)
» Accompanying Notes (PDF)

From Lecture 33 of 18.01 Single Variable Calculus, Fall 2006

Download the complete lectures from this course:

» iTunes U
» Internet Archive

Recitation Video

 

Graph of r = 1 + cos (θ/2)

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Download this video:
» iTunes U (MP4 - 43MB)
» Internet Archive (MP4 - 43MB)

Worked Example

 

Lemniscate

 

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