Example Problems For How To Graph Polar Equations (Calculus 2)
In this video we look at practice problems of graphing 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 graphing basic polar equations first, and then we look at one example of graphing a more complex polar equation using points and symmetry, and the rest of the examples focus on being able to identify special polar equations and graphing them with a quick sketch.
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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 Example 1: r=3 and r=-2
2:23 Example 2: θ=2π/3 and θ=-π/4
5:31 Example 3: r=2secθ and r=-3cscθ
8:13 Example 4: r=2cosθ and r=-4cosθ
11:16 Example 5: r=3sinθ and r=-sinθ
13:33 Example 6: r=1-sinθ (Using Points & Symmetry)
27:57 Example 7: r=1+2sinθ (Quick Sketch)
34:25 Example 8: r=3-3cosθ (Quick Sketch)
39:04 Example 9: r=2cos(6θ) (Quick Sketch)
44:07 Example 10: r^2=9sin(2θ) (Quick Sketch)
47:40 Outro
📝 Lesson Video For These Examples: • Graphing Polar Equatio...
⏩ Next Lesson: • Slope & Tangent Lines ...
📺 Calculus 2 Playlist: • Calculus 2
📺 Calculus 1 Playlist: • Calculus 1
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