How to Graph Polar Equations (Calculus 2 Lesson 47)

In this video we learn how to graph polar equations. This includes polar equations that represent basic polar graphs such as lines and circles, as well as more complex and special polar graphs such as limacons with an inner loop, cardioids, limacons with a dimple, convex limacons, rose curves, and lemniscates. We look at a method that will allow us to graph any polar equation by plotting points and making use of symmetry, and then we look at rules to help us quickly sketch special polar graphs by recognizing the form of a polar equation.

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This video series is designed to help students understand the concepts of Calculus 2 at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with the goal of each video being shorter than the average school lecture!

Calculus 2 requires a solid understanding of calculus 1, precalculus, and algebra concepts and techniques. This includes limits, differentiation, basic integration, factoring, equation manipulation, trigonometric functions, logarithms, graphing, and much more. If you are not familiar with these prerequisite topics, be sure to learn them first!


Video Chapters:
0:00 What are Polar Graphs? (Intro)
2:10 Graphs of r=a & θ=a
4:50 Graphs of r=a*secθ & r=a*cscθ
8:19 Graphs of r=a*cosθ & r=a*sinθ
10:44 Graphing Using Points & Symmetry
12:37 Example: Graphing r=1+cosθ (Points & Symmetry)
26:08 Limacons With Inner Loop
30:36 Cardioids
32:25 Limacons With Dimple
34:33 Convex Limacons
37:11 Rose Curves (cosθ)
40:34 Rose Curves (sinθ)
44:58 Lemniscates
47:56 Outro


Examples Video:    • Graphing Polar Equations Examples | C...  

⏩ Next Lesson:    • Slope & Tangent Lines of Polar Curves...  

Calculus 2 Playlist:    • Calculus 2  

Calculus 1 Playlist:    • Calculus 1  


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