How to Convert Polar Equations to Rectangular Equations & Vice Versa (Calculus 2 Lesson 46)

In this video we learn how to convert from polar equations to rectangular equations and how to convert from rectangular equations to polar equations. We first discuss how polar equations and rectangular equations are related despite being rooted in different coordinate systems, and then how to convert between them since they are related. We look at several examples of converting between polar and rectangular in both directions, explaining each step along the way.

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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 Review of Rectangular Equations
2:08 What are Polar Equations?
4:10 Rectangular vs Polar Equations (Graphically)
10:32 Conversion Formulas
14:30 Example: r=3 to Rectangular
17:10 Example: θ=π/3 to Rectangular
18:46 Example: r=4secθ to Rectangular
20:48 Example: r=5cscθ to Rectangular
22:55 Example: r=2sinθ to Rectangular
28:21 Example: x=9 to Polar
29:28 Example: y=13 to Polar
30:32 Example: x^2+y^2=10 to Polar
31:19 Example: x^2+y^2+8y=0 to Polar
32:44 Example: 3xy+2=0 to Polar
34:30 Example: y^2=9x to Polar
36:49 Outro


Examples Video:    • Converting Polar Equations & Rectangu...  

⏩ Next Lesson:    • Graphing Polar Equations | Calculus 2...  

Calculus 2 Playlist:    • Calculus 2  

Calculus 1 Playlist:    • Calculus 1  


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