The polar coordinate system are an important part of Multivariable Calculus, where the idea of polar coordinates is extended into three dimensions in the Cylindrical and Spherical Coordinate systems.
Even if you are not continuing on to Math 283 (I'm talking to you, Bio majors!), polar coordinates show up in medical applications as well.
Here's an example: Eyeballs are obviously round, so trying to describe their features using a rectangular grid doesn't make much sense. One of the methods ophthalmologists use to analyze the shape and irregularities in a cornea involves a scan (see below) that shows results on a polar grid. This polar grid is what we'll be looking at in this section.
Basics of Plotting and Converting Polar Points. Note: These Kahn Academy videos provide a kind of simplistic (precalculus) presentation but give a decent rundown of the rectangular to polar to rectangular conversion equations and how to use them.
Polar graphs. After you understand how polar and rectangular points work, move on to graphing polar equations.
Handouts:
Polar Graph Paper - Note: I'm personally not a fan of using polar graph paper, since you have to learn to see polar superimposed on x,y-axes when you move into Multivariable Calculus. That being said, using it can help if you're having trouble visually the various angles, and how the r-value of a polar point fits in.
Summary of (some) Polar Curves
Videos on Graphing
Polar Graphing using Desmos (quick) and Desmos (more details)
Assigned Problems:
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Section 11.2 [12.2] Polar Equations
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1st Edition page
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3rd Edition page
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· General
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1 – 6 all
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1 – 6 all
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· Points (I suggest you graph each point as well as do the conversions)
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9, 11, 13, 15, 17, 19, 23, 25
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9, 11, 13, 25, 27, 29, 33, 35
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· Graphs (Do these by hand, by making a table. Use Desmos to check.)
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37, 41, 47, 53
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53, 56, 63
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· Graphs (Identify graphs by evaluating a few key points at 0, pi/2, pi, 3pi/2, 2pi.)
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89
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91
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· Graphs (Use Desmos, observe how the coefficient of theta affects the number of petals)
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95, 96, 97, 98, 99
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97, 98, 99, 10, 101
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· Graphs (Reason out what is happening to r as theta increases)
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100, 101
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102, 103
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